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課程來源:MIT
     

8.06 量子物理III2005年春季

8.06 Quantum Physics III, Spring 2005

譯者:黃熹微

編輯:劉慕華、洪曉慧

Energy levels in a certain time-dependent three state system.

以上是與時間有關的三態系統能級圖,其中有兩個非對角矩陣元素α,而第三個為零,此圖涉及球諧振子和 n=3 時的斯塔克效應。(圖片由Krishna Rajagopal教授提供。)

課程重點

本課程包括了一份相關閱讀資料的列表,一份完整的作業以及整個學期專題的資訊。

課程描述

本課程與前期課程,即8.05 量子物理II8.05: Quantum Physics II一起,包含了自從現代物理學以來的量子物理學的應用。本課程的課題包括單元、時間無關近似方法、帶一個和兩個電子的原子、磁場中的帶電粒子、散射以及時間相關擾動理論。在這個學期(即第二學期),學生需要研究並撰寫一篇課題與8.058.06內容相關的論文。

 

技術需求

推薦使用Microsoft® Powerpoint® software 查看本課程站點的ppt文檔。免費軟體Microsoft® Powerpoint® viewer software 也可以用來查看ppt文檔。可以藉由訪問Comprehensive TeX Archive Network (CTAN) TeX Users Group Web site獲得查看本課程站點tex文檔的軟體。

 

教材

Griffiths, David J.《量子力學導論》Introduction to Quantum Mechanics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2005. ISBN: 0131118927. (必需)(Required)

 

Cohen-Tannoudji, Claude.《量子力學》Quantum Mechanics. 2 vols. New York, NY: Wiley, 1977. ISBN: 0471164321. (必需) (Required)

 

Sakurai, J. J.《現代量子力學》Modern Quantum Mechanics. Reading, MA: Addison-Wesley Pub., 1994. ISBN: 0201539292. (推薦使用;本書有些深奧)(Recommended if you like it; somewhat advanced)

 

Shankar, Ramamurti.《量子力學原理》Principles of Quantum Mechanics. 2nd ed. New York, NY: Plenum Press, 1994. ISBN: 0306447908. (推薦使用;本書有些深奧)

(Recommended if you like it; somewhat advanced)

 

Ohanian, Hans.《量子力學原理》Principles of Quantum Mechanics. Upper Saddle River, NJ: Prentice Hall, 1989. ISBN: 0137127952.

 

必備先修課

必須完成量子力學II (8.05)的課程並獲得C以上的成績才能選擇8.06課程。

 

評分

成績將藉由一個加權平均值來得到,即包括習題集、課堂內進行的期中考試、一份學期論文和期末考試。教授可以根據課堂表現,進步,努力和其他能力的展現改變等級。

 

活動

百分比

習題集

30%

期中考試

15%

學期論文

20%

期末考試

35%

 

 

習題集

習題集是8.06中非常重要的一個部分。我們相信靜下心來嘗試自己解決問題,不僅能幫助你深入地學習相關知識,也能使你們的基本分析能力增強,這些對你們成為一名在科學領域的成功專業人才是很有幫助的。我們認識到學生能從相互對話和工作中受益良多。因此,我們鼓勵每一個選修8.06的學生,能自己去嘗試解決每一個問題,或者能藉由和別人討論和合作,在得到完全深入地理解後,能夠解決這些問題。你繳交的答案必須反映出你自己在其中的工作。解答不應當抄襲或者複製別人的工作。剽竊是一個嚴重的過錯並且很容易被識別出來。所以不要繳交不屬於你自己的工作。

學期論文

1)專題摘要)

課題範圍教學時程、相關閱讀資料、相關資源

 

(見教材)

下表列出了涵蓋本課程九個主題的閱讀作業,欲知詳細資訊請見本閱讀作業部份個別作業專題:

見技術需求

有些課題與通常和量子物理III同時進行的課堂實驗8.13-8.14:實驗物理學I 和II8.13-8.14: Experimental Physics I & II 初級實驗室 Junior Lab的內容相關。

 

 

課程單元

相關作業

閱讀資料

相關實驗

1

自然單元

作業1

 

 

2-4

簡並費米系統

Degenerate Fermi Systems

作業2

Griffiths,5.3
Cohen-Tannoudji,XI章 補充F

 

4-8

磁場中的帶電粒子

Charged Particles in a Magnetic Field

作業2, 3, 4

Griffiths, section 10.2.4
Cohen-Tannoudji,
VI章 補充E

 

9-12

時間不相關微擾理論

Time-independent Perturbation Theory

作業4, 5, 6

Griffiths,6
Cohen-Tannoudji,XI章 包括補充A-D
Cohen-Tannoudji,
XII
同見Shankar,17章 和Sakurai,5.1-3

氫原子的發射光譜光學  

Optical Emission Spectra of Hydrogenic Atoms

 

21釐米無線電天體物理學

21-cm Radio Astrophysics

 

塞曼效應

The Zeeman Effect

 

銣蒸汽的光抽運

Optical Pumping of Rubidium Vapor

 

X-射線物理學X-Ray Physics

 

消多普勒鐳射光譜學

Doppler-Free Laser Spectroscopy

13-15

變分和半經典方法

Variational and Semi-classical Methods

作業7, 8

Griffiths,7, 8
Cohen-Tannoudji,XI章補充E, F, G
同見Shankar,16章和Sakurai,5.4

超導電性 Superconductivity

16-18

絕熱近似法和Berry

The Adiabatic Approximation and Berry's Phase

作業8

Griffiths,10

 

19-23

散射Scattering

作業9, 10

Griffiths,11
Cohen-Tannoudji,VIII
同見Shankar,19

弗蘭克-赫茲實驗

The Franck-Hertz Experiment

 

盧瑟福散射

Rutherford Scattering

23-24

時間相關擾動理論

Time-dependent Perturbation Theory

選做的習題集

Griffiths,9
Cohen-Tannoudji,XIII

同見Shankar,18 章和Sakurai,5.5-8

銣蒸汽的光抽運

Optical Pumping of Rubidium Vapor

 

消多普勒鐳射光譜學Doppler-Free Laser Spectroscopy

25

量子計算Quantum Computing

選做的習題集

 

核磁共振量子資訊處理

Quantum Information Processing with NMR


作業

相關的閱讀材料來自於顯示在列表中的教材,這些讀物有助於學生理解習題。

 

作業

相關閱讀資料

作業1 (英 PDF)

Griffiths,5.3
Cohen-Tannoudji,XI, 補充F

作業2 (英 PDF)

Griffiths,10.2.4
Cohen-Tannoudji,VI, 補充E
Sakurai,
130-139

作業3  (英 PDF)

Griffiths,10.2.4
Cohen-Tannoudji,VI, 補充E
Sakurai,
130-139

作業4 (英 PDF)

Griffiths,6.1, 6.2
Cohen-Tannoudji,XI

作業5  (英 PDF)

Griffiths,6
Cohen-Tannoudji,XI, 補充A-D

作業6  (英 PDF)

Griffiths,6

Cohen-Tannoudji,XI, 補充A-D,XII

作業7 (英 PDF)

Griffiths,7, 8
Cohen-Tannoudji,XI, 補充E, F, G

習作業8 (英 PDF)

Griffiths,8, 10
Haxton, W. C.〈太陽中微子問題〉The Solar Neutrino Problem.《天文和天體物理年鑒評論》Annual Review of Astronomy and Astrophysics 33 (1995): 459-503.

作業9 (英 PDF)

Cohen-Tannoudji,VIII
Griffiths,11
Ohanian,11

作業10 (英 PDF)

Cohen-Tannoudji,VIII
Griffiths,9, 11
Ohanian,11

選做的習題集  (英 PDF)

 

專題

(見技術需求)

專題摘要

每一個選修8.06課程的學生都要研究、撰寫和發表一篇與8.058.06課程有關的內容的主題的短篇論文。論文可以說明一個物理現象,也可以深入分析課程所涵蓋的概念或者習題。這應當基於學生自己的計算或者到圖書館的調查。論文應該依據主要刊物上文章的風格和格式,並能針對聽眾是8.06課程的學生。

撰寫、編輯、修改和發表的能力都是這個專案不可缺少的部分。你們每個人都要找到另外一個同學,校對你們的草稿,然後根據校對同伴的建議,準備一份最終稿。我們將提供針對LATEXRevtex樣式的範本(被《物理評論》使用),這樣,你們就能完成一份形式完整的,可發表的論文。我們也將安排一個 LATEX指南,很可能在四月份的某一天。

你們繳交的第一份草稿上面必須標有你們校對同伴的評注。這份草稿接著將由一個寫作助教(如下所示)批閱,然後返還給你們。在第一次草稿截至日期的兩周後,你們將繳交你們的最終稿。論文的分數將由你們工作的思考水準,表達效果和論文風格來決定。另外,你作為校對人員,對校對工作的認真程度以及是否提出建設性意見,也會成為分數評定參照的一部分。論文最後的分數將占8.06最終成績的20%

因為8.06是一個CI-M(密切溝通的主修課程)(Communication Intensive in the Major),為了藉由這門課程,你必須在論文上得到等級C或以上。如果你沒有達到這個要求,就不能獲得完整的成績,除非你能修改你的論文直到滿足至少達到C的要求,到那個時候,你才能得到包含20%學期論文分數的最終的課程成績。

當一位物理學者在寫一篇論文時,他(或她)經常邀請一些同事對他(或她)的初稿進行評論。在被像《物理評論》這樣的刊物接收前,最終稿還將被一個或者幾個相同水準的人員進行匿名形式的評審。這種正式和非正式的評論過程是為了促進作者與其他同事進行更深入的交瀏思想。你們的目標就是寫一篇關於量子力學現象或者問題的論文,你們應該和學習8.06的同學們進行有效的和清晰的交瀏,他們也就是你們的同事。不要與老師交瀏,儘管他們非常願意聽取你的意見。一定要與你的同事交瀏。如果你的同事不能理解你寫的內容,你就是不成功的。注意,你是為你的同事寫的,這比為教授寫的標準還要高。準備的題目應該是足夠清晰和有邏輯性的,它對於你們同事來說是陌生的,他們必須經過清晰的思考和深入的理解。這些是寫一篇好論文的必備條件。

將會有四個寫作助教幫助你們撰寫,編輯和準備你們的論文。在329日,你們每個人都要藉由電子郵件與一個寫作助教聯繫(看下面的進度)。你們需要儘快安排時間見面。如果有問題要及時向他們尋求幫助。他們將審核你們的提案和論文的概要。校對後的第一份草稿,也必須經過他們的批改。在你寫你論文的時候,可以要求你的助教幫助你論文中的一部分。把寫作助教當作你們的教練。他們是為你們服務的,並且對這方面很精通。如果你希望在329日之前得到他們的幫助,請將你的論文提案和你的校對同伴的名字發送過來,然後將會安排一個寫作助教來幫助你。

在你繳交最終的論文時,它已經被你的同伴校對過,你也要有足夠的時間來補充寫作助教的建議。以前的學生發現,藉由這個過程可以使論文水準得到極大的提高。根據以前的經驗,你們繳交最終的論文後,絕大多數同學的物理寫作水準會有很大的提高。如果這樣的論文沒有被發表會是很遺憾的。我們將以自己的標準出版一本刊物,收錄你們的論文。其中有兩點要求:(1)使用LATEX範本的電子版論文。(2)成績為B或者以上的論文,達到這兩點,才會被發表。依據這些要求,我們希望創建一本屬於你們自己的論文集。這本刊物將會發給你們,這樣你們不僅可以看到自己的,還可以看到其他同伴的工作成果。

2) 論文的進度和期限

你們應該利用學期開始的時間考慮可能的題目和選擇校對同伴。你的校對同伴必須是學習 8.06 的學生,並且他(或她)的論文題目不能和你的相關的。下面給出了推薦題目的列表,你也可以自由選擇其他題目,但必須先得到 Rajagopal 教授的認可。 到春季假期結束的時候,你應該有一個很好的想法,決定寫什麼主題,並且正在進行相關知識的學習。如果需要計算,你也應該正在做一些計算。到期中時完成所寫物理內容的構思,並且完成相應的計算。接下來就要撰寫提案:

你的提案必須在 329日之前完成。 它要包括題目,一段描述內容的短文,論文提案的概要,一份參考書目清單,校對同伴的名字,以及你的名字和電子郵件。

接下來將有一個寫作助教與你聯繫。 他們可能同意你的提案,也可能要求你進行修改。你要盡可能多的與他們接觸 (即使他們接受了你的意見)。 無論是誰,如果在遞交第一份草稿前,沒有與寫作助教的交瀏過,都將會受到懲罰。

你的第一份校對草稿截至於412日星期二。這意味著你必須在此時間以前,把第一份草稿交給校對同伴,這是為了給校對同伴足夠的時間去修改。每個人都應該在415日之前去見寫作助教,這樣可以得到關於你們第一份草稿的修改意見。實際上,如果 AB 編輯,而且 BA 編輯,我將保證 AB 有相同的寫作助教,並且建議你們一塊兒去見他(或她),同時聽取你們的論文的評審建議。你們將在你們的論文達到寫作助教的要求時得到回復的第一份草稿。

一份你的最終的優美的論文的列印本繳交日期將截至於本學期的426日星期二。可以想像成把你的論文繳交給 8.06《物理評論》。如果編輯(Rajagopal教授) 給你的是一個肯定的回復(例如,成級為B或以上),你就可以繳交電子版的論文的發表,同時也可以得到一份 2005年的《物理評論》。

3) 論文的性質

本論文的目的是對於量子力學中某一個問題 或者現象給出一個詳細的介紹。

主題為問題的論文,可以與習題集中出現的問題相類似,但必須是經過精心準備的。例如,在8.05的諧振子內容中簡要介紹到的相干態。同學們可以深入鑽研相干態的更深內容,描述相干態,解釋相干態的有關問題,並且給出一些應用的例子。 這樣的論文應該類似於8.05課本中的一些章節。寫論文時首要選擇的參考書目,應該是現有的量子力學教材以及可以找到的有關原著。

主題為現象 的論文應該依據8.06的知識來介紹現象並解釋產生的原因。例如,當我們在8.05的最後部分學習全同粒子時,簡單提到了氫的同素異形體為 鄰位氫 和對位氫。學生必須知道它們是什麼,根據費米-狄拉克統計瞭解它們的性質,描述它們在早期量子力學的歷史中扮演的有趣角色。再次重申,首要的參考書目是課本,也可能是關於這方面的現代物理教材,量子物理學史,以及相關原著。

問題為主題的論文必須有一部分是你自己的計算。以現象 為主題的論文可以包含一些圖書館查詢到的資訊。 對於其他任何材料,都必須給出參考書目。不要剽竊。無論是誰如果企圖從主瀏刊物上直接引用材料,都會發現要找到一本與8.06水準相當的量子物理學刊物是非常困難的。

我們鼓勵同學們寫論文時,對8.058.06課上所介紹的一個問題或者一種現象進行擴展。如果這樣做,你們將在現有的基礎上進行更深一步的學習。同學們也可以選擇課堂上沒有講到的內容作為主題,但是關於量子力學方面的說明,學習過8.058.06的學生應該可以理解。

請不要嘗試選擇一些偏僻的、困難的或者有爭議的主題。如果想藉由這種選題得到教授的賞識,必將適得其反。在量子力學中有很多深奧的,有趣的,具有挑戰性的題目。

論文的長度應限制在 8-15(如提供的LATEX範本) 。這些限制是嚴格的。

鼓勵同學們運用方程和圖像,這些可以幫助你表達,這與在刊物和教科書中的運用是一樣的。

4) 可選擇的主題

歡迎同學們提出自己的課題。但你應該給 Rajagopal 教授發一封簡短的電子郵件,概括介紹一下你所寫的課題。沒有必須的期限,但是要注意應該在329日完成提案。繳交提案的以前,你應該得到了Rajagopal 教授對你的課題的許可。(注意:你們的寫作助教仍然可能要求你們修改提案。)

下面是列出了可能的課題。對於其中的大部分,Rajagopal 教授或者劉教授將談到如何開始閱讀這些課題。然而不會針對全部都說明。

1. 相干態。 Coherent states.

2. 氫的同素異形體。The allotropic forms of hydrogen

3. 核磁共振。舉例,你可以從8.05中我們沒有講到的地方開始,解釋核磁共振如何應用到文中所涉及到的特殊實驗。 Nuclear Magnetic Resonance. For example, you might take off from where we stopped in 8.05 and explain how NMR is applied in a particular experimental context.

4. 磁單極子,規範不變性,以及磁單極子中的磁核的狄拉克量子化條件。 Magnetic monopoles, gauge invariance, and the Dirac quantization condition for the magnetic charge of a magnetic monopole.

5. 磁通管的散射。Scattering off a magnetic flux tube.

6. Bell 定理――經典力學可以模仿量子力學嗎? Bell's theorem - can classical mechanics imitate quantum mechanics?

7. 真空中的中微子的振盪,。超出我們在8.05課程中所學的。Neutrino oscillations in vacuum, beyond what we covered in 8.05.

8. K介子和B介子的振盪現象,超出我們8.05課程中所學的。 Oscillation phenomena involving kaons and/or B mesons, beyond what we covered in 8.05.

9. 太陽中微子問題。The solar neutrino problem.

10. Levinson 定理 散射的相移是如何與勢阱中的束縛態聯繫起來的。Levinson's theorem - how the scattering phase shift is related to the number of bound states in a potential.

11. 原子結構的殼模型。The shell model of nuclear structure.

12. 氘核的性質。The properties of the deuteron.

13 238 Uα-衰變 The α-decay of 238 U.

14. 雙原子分子的轉動光譜和振動光譜。The rotational and vibrational spectrum of diatomic molecules.

15. 氫原子的 SO(3) × SO(3) 動力學對稱性。Dynamical SO(3) × SO(3) symmetry of the hydrogen atom.

16. n-維諧振子的 SU(n) 動力學對稱性。 Dynamical SU(n) symmetry of the harmonic oscillator in n-dimensions.

17. 超對稱量子力學,超出我們所學的8.05。 Supersymmetric quantum mechanics, beyond what we did in 8.05.

18. 弱磁場,中等強度磁場 和 強磁場中的塞曼效應。The Zeeman effect in weak, intermediate and strong magnetic fields.

19. 氫原子的蘭姆位移 相對論量子力學必須被量子場論代替的依據。(這是一個課題的案例,你不必給出這個效應的完整的來源,但是對你感興趣的物理學史的部分,你應當著重闡述其中的量子力學部分,同時描述相應的試驗和完整的歷史。)The Lamb shift in hydrogen - evidence that relativistic quantum mechanics must be replaced by quantum field theory. (This is an example of a topic where you will not be able to give a complete derivation of the effect, but where those of you interested in the history of physics could write a paper which explains the quantum physics more qualitatively while at the same time describing the experiments and the history in full.)

20. 質子,中子和相關粒子的非相對論誇克模型。 The non-relativistic quark model of the proton, neutron and related particles.

21. 同位旋 基本粒子的量子對稱。Isospin - a quantum symmetry of elementary particles.

22. 氫原子的 21 cm結構以及在天體物理學中的地位。The 21 cm. line of hydrogen and its role in astrophysics.

23. 凱西米爾效應。 The Casimir effect.

24. 量子力學中費曼路徑積分的提出,你可以應用它去解決幾道我們以前用其他方法分析的問題。Feynman's path integral approach to quantum mechanics, and its application to several problems of your choice which we have previously analyzed using other methods

25. 處於激發態的氫原子之間的範德瓦爾斯力。The van der Waals force between hydrogen atoms in excited states.

26. 量子計算?(不能只是為了寫量子計算而寫一篇的論文。如果你沒有自己的興趣點,包含對量子計算在執行過程中的一些見解,量子力學在其中的如何運用,以及遇到的困難等等,就不要在其中選擇一個課題。注意,我不贊成以Grover或者Shor演算法作為唯一的課題,在本課程學期結束你們就會對此有所瞭解。) Quantum computing? (You may not write a paper that purports to be about "Quantum computing". You may only choose a topic within this area if you have a focussed idea, perhaps involving presentation of one of the ideas for implementation of a quantum computer, the quantum mechanics of the implementation, the difficulties, etc. Note also that you may not write a paper whose sole purpose is the presentation of Grover's and/or Shor's algorithms, since you will see those in lecture at the end of the semester.)

27. 量子遠距傳物。 Quantum teleportation.

28. 量子密碼學。 Quantum cryptography.

29. 玻色-愛因斯坦凝聚。Bose-Einstein condensation.

30. 整數量子的霍爾效應(你可以利用許多超出我們課堂上講到的方法。) Integer Quantum Hall Effect (There are a number of ways you could go beyond what we do in lecture.)

31. 兩維系統中的郎道傳導率。Landauer conductivity in two dimensional systems.

32. 光子晶體。 Photonic Crystals.

33. 量子點。 Quantum Dots.

34. 應用 deHaas van Alphen 效應作為測量金屬費米子表面外形的工具。 The deHaas van Alphen effect as a tool for measuring the shapes of fermi surfaces in metals.

35. 週期勢和能帶結構。Periodic potentials and band structure.

36. 關於光量子和黑體輻射光譜的量子統計力學的入門。(你的闡述也應該包括普朗克如何在前期發現量子力學,或者黑體輻射光譜是如何在宇宙三度背景輻射中呈現出來的。) An introduction to the quantum statistical mechanics of photons and the spectrum of black body radiation. (You could also include an account of how Planck was led to discover quantum mechanics in the first place, or of how the spectrum of black body radiation appears in the cosmic three degree background radiation.)

37. 量子力學的密度矩陣形式,以及量子統計力學。 The density matrix formalism in quantum mechanics, and quantum statistical mechanics.

38. 光抽運,微波激射器,鐳射。Optical pumping, masers, lasers.

39. 微波激射器在天體物理學的應用Masers in astrophysics.

40. 半經典近似的有趣應用。 Interesting applications of the semiclassical approximation.

41. Ramsauer-Townsend效應The Ramsauer-Townsend effect.

42. 約瑟夫森效應The Josephson effect.

43. Wigner-Eckart定理The Wigner-Eckart theorem.

44. 二維分數統計Fractional statistics in two dimensions.

 

45. 緊態及其應用Squeezed states and applications.

46. 魏格納函數及其應用Wigner functions and applications.

47. 隧道效應,超出了課堂內容。歐幾裏得逼近法;非零溫度效應Tunnelling, beyond the discussion in class. The Euclidean approach; effects of nonzero temperature

48. 量子耗散的微觀起源和效應,例如隧道效應The microscopic origin and effects of quantum dissipation, for example on tunnelling.

49. 逆散射及其在孤立子上的應用Inverse scattering method and its application to solitons.

 

5) 寫作技巧

下面是一些你可能覺得有用的技巧。

5.1)結構

盡可能早的確定一個明確的主題。改變主題也可以,但你會發現為了使敍述清晰,將會有大量的修改。

在充分學習和理解要寫的物理知識後再動筆。 你應該在春季假期時做這些事情。這將保證你在開始寫之前,有一個非常明確的主題。你會發現這樣組織你的論文會比較容易。

確保要清晰地表達論文的主要內容。 這對於科學寫作是非常重要的,因為讀者很容易陷入細節中而找不到主題。主題思想在論文的格式中應該是突出的,也可在導言或摘要中提到。

要寫摘要,若有可能,也要寫結尾總結。

做完摘要後,不要害怕在起草之前準備前面的部分。如果你對後面部分的理解比前面的部分更深入,也可以從後半部分寫起。這些可以幫助你從整體上把握和說明前半部分。 這麼做可以幫助你思考如何理解和描述前面的部分。

5.2)風格

在思考風格和結構時,要記住你寫的是一篇科學論文而不是一篇文學作品。有代表性的偉大文學作品都有很多含義,不同水準的人可以從不同的角度瞭解,不同時期和不同背景的讀者也有不同的理解。它會經常提及到其他偉大的作品。許多年後,人們理解這些偉大作品的含義時,已經超出了作者自身的意圖。相反,科學論文的主要意圖是把你的思想清晰地傳達給讀者,不能模棱兩可,不能有歧義。你的目的是保證每一個讀者都能準確理解你的意思,雖然他們可能有不同的知識背景。這意味著清楚和精確是很重要的。你應該保證,你所寫的每一個句子,都不會使讀者產生誤解。甚至當讀者企圖曲解你的意思。

運用你最熟悉的表達語態。我將證明我們將證明它將被證明都是可以的。由於一些不確定的原因,有些學生認為人稱代詞應該被禁用,而被動語態是必須的。沒有任何知識比事實還重要。優秀的科學著作應該是活生生的和引人注目的。你的論文應該講述一個物理故事。我認為過度使用被動語態就會失去活力,變得單調乏味。清晰和準確是首要的,但不要落入這樣的思想陷阱,認為只有感動了讀者,才能達到好的效果。

儘量去引導你的讀者,激發他們的興趣。如果有些知識需要他們理解,還要加強他們的物理知識背景。把他們吸引到你所講的故事中,並得到一個引人注目的結論。

所有這些我給你們的建議,在以後的日子中,當你們準備一次演講或者研討會時,就會覺得是非常重要。

5.3)一些細節Some Details

嚴格保證符號的一致性,儘管有時冒著重複的風險。

詳細說明你用到的每一個量。

避免不明確的闡述,比如這說明,要用“Eq. 4.1 說明代替。 這兒的LATEX 命令 label ef 是有用的。

6) 關於校對的更多事項

正如專案摘要中所要求的,每一個人都要作為你同伴的校對(注意:如果你找不到一個合適的同學作為你的校對,諮詢Rajagopal教授。他收到請求後,會及時為你安排。 在329日,你必須給出校對同伴的名字,這是提案中的一部分)。完成你的第一份草稿後,交給你的校對同伴進行校對。為了能在412日星期二繳交第一份校對過的草稿,你必須給校對同伴留下足夠的時間校對。

當你校對搭檔的草稿時,首先應該表揚這篇文章的優點。如果作者有具體的要求(例如:請仔細查看對你有用的某些理論知識),就應該去認真的研究這部分內容。除非作者要求,不要把校對重點放在文章的撰寫細節上。(當然,也要記下偶然遇到的這些問題,但記住這不是你的主要目的。而且對於這方面的評審,作者也不應該依賴你。)集中精力幫助作者校對論文的內容,結構和邏輯性。不要只注重批評。對於所遇到的問題,要提出一些可以解決的建議。

在校對搭檔的論文時,應該考慮下面的一些問題:

論文的主要論點是什麼?

論文是如何吸引人的?是否闡述了主題的重要性?

論點的細節是怎樣處理的?是系統性越高越好;還是越具體越好?比較結果,找到其中造成這樣的結果的關鍵的優點。

為了使論文的邏輯清晰,是不是應該把文章分成幾個部分?每一部分意思是否跟前一部分聯繫緊密?段落是否銜接得當?

在文章的開頭,是否可以展現出整篇文章的清晰脈絡?

是否所有的引用材料都注有出處? 如果論文的觀點並不是作者計算的結果,也不是在課上遇到過的,你能看出作者是如何收集這些觀點的嗎?

對於所有的新術語,是否給出了準確的定義,並且前後一致。

如果論文提到了問題的解決辦法,那麼它所依據的理論是什麼?是否真正理解每一個觀點以及整體的解決方案?是不是理論的每一部分都能被證實(或藉由文章中提到的計算方法,或藉由8.058.06的文獻資料,找到論點的證明)。是否漏掉了一些可以使論證更充分的東西?

如果論文描述了一種現象,你是否理解它的描述?現象的本質是否被清楚的表達出來?這個現象能被成功表達的優點在哪兒?是否清楚作者提到的對於現象的量子力學解釋?為了能夠更好的理解這一現象,你希望作者還要做些什麼?

7) LaTeX範本

LaTeX (和它的前身TeX)在學術界和技術界被廣泛應用於出版.它們和標記語言HTML®一樣,告訴了處理器如何建構數學表述文字排版格式。這個專案的目標之一,就是為了讓你們體驗編寫物理學論文的出版。當練習物理學家繳交論文給《物理評論》評審,他們就是這樣發送一份LaTeX格式的檔給編輯部的,並且,可能還有一些圖形附件。如果你希望你的論文能夠被出版,你就需要這樣做。

許多8.06的學生曾經接觸過LaTeX;有的則沒有。為了公平起見,為了使你可以發表最終的論文、我們將在網上提供供你可以下載一個範本。LaTeX本身已成為麻省理工伺服器的標準軟體.

你們中可能有許多電腦盲——甚至到目前為止還不如Rajagopal教授或者劉教授,只需要下載範本,用你喜歡的編輯器(例如emacs)打開範本,然後使用LaTeX處理標題、頁註腳、參考文獻、方程、打開或關閉數學符號、方程標籤、跳位字元等等。你可以藉由切割範本文本並插入你自己的檔構建出你的論文。

為了使學生獲得所有必要巨集指令,那些巨集指令已經安裝在麻省理工伺服器,可能有必要先鍵入: add newtex[注:三年前這是必要的,但Rajagopal教授認為現在是沒有必要的。]

您應該首先下載範本、並確定你們成功得到了LaTeX、製作輸出像我將發佈在伺服器一樣的範本的列印本。

為了做到這些,你需要下面這些命令:

latex filename.tex 將運行LaText類型設置程式,從而生成你根據輸入檔排版後的輸出。如果你的LaTeX檔有錯誤,日誌檔filename.log將包含有用的錯誤資訊。當LaTeX運行成功後,它的輸出檔為filename.dvi,這裏的dvi的含義是設備無關。(注,你需要對這個檔兩次運行LaTeX,以便讓所有的參考文獻專案和方程式數目都能正確出來。)

xdvifilename.dvi將顯示出你的輸出檔的正確形式。

dvipsfilename.dvi會把一個dvi檔轉換為一個附錄檔,並把它發送到印表機,然後刪除後記檔。如果不是,你希望保存一個後記檔而不是列印它,使用dvips -o filename.ps filename.dvi。這樣做的原因之一是,你可以使用ghostview(gv)命令查看輸出而非xdvigv是一個比xdvi更複雜的瀏覽器。(最後注:gv默認非antialias反別名以節省時間。它可以在gv中打開或關閉,或者你可以用 -antialias標誌調用gv自動這樣處理。)

模本將提供包含的後記圖像。如果你知道如何在後記中製作插圖,模版說明如何在你的論文中合併它們。如果你不想這麼麻煩,你可以手繪或者使用你最喜歡的圖形包,簡單的將它們釘在你論文的最後.注意,無論如何,如果你希望你的最終論文能夠被發表,你就必須準備使用LaTaX範本,包含封裝像在範本裏面做的一樣的後記檔的圖形。

範本使用一個巨集,叫做BoxedEPS,來合併封裝後記圖形。這個巨集指令可以在麻省理工伺服器上瀏覽,為了安全起見,我們必須將在供你下載的同時,下載你自己的範本。

我們強烈鼓勵同學們使用LaTeX溝通.同樣,我們大力提倡這方面經驗較少的同學使用LaTeX導航以幫助他們。

論文範例

8.06 學期論文範例  8.06 Sample Term Paper (英 PDF)

 

支援檔

BoxedEPS (TEX)

論文範例Sample Paper (TEX)

能級  Energy Levels  (英 PDF)

 

 

 

以下為系統擷取之英文原文

8.06 Quantum Physics III

Spring 2005

Energy levels in a certain time-dependent three state system.

Energy levels in a certain time-dependent three state system with two off-diagonal matrix elements α and the third zero, a spherical harmonic, and the Stark effect for n=3. (Image by Prof. Krishna Rajagopal.)

Course Highlights

This course features a list of readings, a complete set of assignments, and information on a term-long project.

Course Description

Together, this course and its predecessor, 8.05: Quantum Physics II, cover quantum physics with applications drawn from modern physics. Topics in this course include units, time-independent approximation methods, the structure of one- and two-electron atoms, charged particles in a magnetic field, scattering, and time-dependent perturbation theory. In this second term, students are required to research and write a paper on a topic related to the content of 8.05 and 8.06.

Technical Requirements

Special software is required to use some of the files in this course: .tex.




*Some translations represent previous versions of courses.





Syllabus

Amazon logo Help support MIT OpenCourseWare by shopping at Amazon.com! MIT OpenCourseWare offers direct links to Amazon.com to purchase the books cited in this course. Click on the Amazon logo to the left of any citation and purchase the book from Amazon.com, and MIT OpenCourseWare will receive up to 10% of all purchases you make. Your support will enable MIT to continue offering open access to MIT courses.


Topics Covered

Natural Units

Degenerate Fermi Systems

Charged Particles in a Magnetic Field

Time-independent Perturbation Theory

Variational and Semi-classical Methods

The Adiabatic Approximation and Berry's Phase

Scattering

Time-dependent Perturbation Theory

Quantum Computing

Topics covered, in detail (PDF)



Texts

Amazon logo Griffiths, David J. Introduction to Quantum Mechanics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2004. ISBN: 9780131118928. (Required)

Amazon logo Cohen-Tannoudji, Claude. Quantum Mechanics. 2 vols. New York, NY: Wiley, 1977. ISBN: 9780471164326. (Required)

Amazon logo Sakurai, J. J. Modern Quantum Mechanics. Reading, MA: Addison-Wesley Pub., 1994. ISBN: 9780201539295. (Recommended if you like it; somewhat advanced)

Amazon logo Shankar, Ramamurti. Principles of Quantum Mechanics. 2nd ed. New York, NY: Plenum Press, 1994. ISBN: 9780306447907. (Recommended if you like it; somewhat advanced)

Amazon logo Ohanian, Hans. Principles of Quantum Mechanics. Upper Saddle River, NJ: Prentice Hall, 1989. ISBN: 9780137127955.



Prerequisites

You must complete Quantum Mechanics II (8.05) with a grade of C or better before attempting 8.06.



Grading

Grades will be determined by a weighted average of problem sets, a Midterm that will be held in class, a Term Paper, and a Final Exam. The faculty may alter grades to reflect class participation, improvement, effort and other qualitative measures of performance.


Grading table. ACTIVITIES PERCENTAGES
Problem Sets 30%
Midterm Exam 15%
Term Paper 20%
Final Exam 35%





Problem Sets

Problem sets are a very important part of 8.06. We believe that sitting down yourself and trying to reason your way through a problem not only helps you learn the material deeply, but also develops analytical tools fundamental to a successful career in science. We recognize that students also learn a great deal from talking to and working with each other. We therefore encourage each 8.06 student to make his/her own attempt on every problem and then, having done so, to discuss the problems with one another and collaborate on understanding them more fully. The solutions you submit must reflect your own work. They must not be transcriptions or reproductions of other people's work. Plagiarism is a serious offense and is easy to recognize. Don't submit work which is not your own.



Term Paper

Everyone in 8.06 will be expected to research, write and "publish" a short paper on a topic related to the content of 8.05 or 8.06. The paper can explain a physical effect or further explicate ideas or problems covered in the courses. It can be based on the student's own calculations and/or library research. The paper should be written in the style and format of a brief journal article and should aim at an audience of 8.06 students. Writing, editing, revising and "publishing" skills are an integral part of the project, which is described in full in the projects section.

Because 8.06 is a CI-M (Communication Intensive in the Major) Subject, in order to pass 8.06 you must obtain a grade of C or better on your term paper. If you do not succeed in this, you will get a grade of Incomplete until you revise your term paper sufficiently to earn at least a C, and only at that time you will be assigned a final grade based on the breakdown given above.





Calendar

Calendar table. LEC # TOPICS RELATED ASSIGNMENTS
1 Natural Units Assignment 1
2-4 Degenerate Fermi Systems Assignment 2
4-8 Charged Particles in a Magnetic Field Assignments 2, 3, 4
9-12 Time-independent Perturbation Theory Assignments 4, 5, 6
13-15 Variational and Semi-classical Methods Assignments 7, 8
16-18 The Adiabatic Approximation and Berry's Phase Assignment 8
19-23 Scattering Assignments 9, 10
23-24 Time-dependent Perturbation Theory Optional Problem Set
25 Quantum Computing Optional Problem Set




Readings

Amazon logo When you click the Amazon logo to the left of any citation and purchase the book (or other media) from Amazon.com, MIT OpenCourseWare will receive up to 10% of this purchase and any other purchases you make during that visit. This will not increase the cost of your purchase. Links provided are to the US Amazon site, but you can also support OCW through Amazon sites in other regions. Learn more.


Texts

Amazon logo Griffiths, David J. Introduction to Quantum Mechanics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2004. ISBN: 9780131118928.

Amazon logo Cohen-Tannoudji, Claude. Quantum Mechanics. 2 vols. New York, NY: Wiley, 1977. ISBN: 9780471164326.

Amazon logo Sakurai, J. J. Modern Quantum Mechanics. Reading, MA: Addison-Wesley Pub., 1994. ISBN: 9780201539295.

Amazon logo Shankar, Ramamurti. Principles of Quantum Mechanics. 2nd ed. New York, NY: Plenum Press, 1994. ISBN: 9780306447907.

The following table lists the reading assignments for each of the nine topics covered in this course. For more detailed information on these reading assigments, please see the individual assignments in the assignments section.


Table for readings. LEC # TOPICS READINGS
1 Natural Units  
2-4 Degenerate Fermi Systems Griffiths, chapter 5.3

Cohen-Tannoudji, chapter XI Complement F
4-8 Charged Particles in a Magnetic Field Griffiths, section 10.2.4

Cohen-Tannoudji, chapter VI Complement E
9-12 Time-independent Perturbation Theory Griffiths, chapter 6

Cohen-Tannoudji, chapter XI including Complements A-D

Cohen-Tannoudji, chapter XII

See also Shankar, chapter 17 and Sakurai, chapter 5.1-3
13-15 Variational and Semi-classical Methods Griffiths, chapters 7, 8

Cohen-Tannoudji, chapter XI Complements E, F, G

See also Shankar, chapter 16 and Sakurai, chapter 5.4
16-18 The Adiabatic Approximation and Berry's Phase Griffiths, chapter 10
19-23 Scattering Griffiths, chapter 11

Cohen-Tannoudji, chapter VIII

See also Shankar, chapter 19
23-24 Time-dependent Perturbation Theory Griffiths, chapter 9

Cohen-Tannoudji, chapter XIII

See also Shankar, chapter 18 and Sakurai, chapter 5.5-8
25 Quantum Computing  




Assignments

Amazon logo When you click the Amazon logo to the left of any citation and purchase the book (or other media) from Amazon.com, MIT OpenCourseWare will receive up to 10% of this purchase and any other purchases you make during that visit. This will not increase the cost of your purchase. Links provided are to the US Amazon site, but you can also support OCW through Amazon sites in other regions. Learn more.

The related readings from the textbooks shown in the table will help understand the assignments.



Texts

Amazon logo Griffiths, David J. Introduction to Quantum Mechanics. 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2004. ISBN: 9780131118928.

Amazon logo Cohen-Tannoudji, Claude. Quantum Mechanics. 2 vols. New York, NY: Wiley, 1977. ISBN: 9780471164326.

Amazon logo Sakurai, J. J. Modern Quantum Mechanics. Reading, MA: Addison-Wesley Pub., 1994. ISBN: 9780201539295.

Amazon logo Shankar, Ramamurti. Principles of Quantum Mechanics. 2nd ed. New York, NY: Plenum Press, 1994. ISBN: 9780306447907.

Amazon logo Ohanian, Hans. Principles of Quantum Mechanics. Upper Saddle River, NJ: Prentice Hall, 1989. ISBN: 9780137127955.


Assignment files. ASSIGNMENTS RELATED READINGS
Assignment 1 (PDF) Griffiths, chapter 5.3

Cohen-Tannoudji, chapter XI, Complement F
Assignment 2 (PDF) Griffiths, section 10.2.4

Cohen-Tannoudji, chapter VI, Complement E

Sakurai, pp. 130-39
Assignment 3 (PDF) Griffiths, section 10.2.4

Cohen-Tannoudji, chapter VI, Complement E

Sakurai, pp. 130-39
Assignment 4 (PDF) Griffiths, sections 6.1, 6.2

Cohen-Tannoudji, chapter XI
Assignment 5 (PDF) Griffiths, chapter 6

Cohen-Tannoudji, chapter XI, Complements A-D
Assignment 6 (PDF) Griffiths, chapter 6

Cohen-Tannoudji, chapters XI, Complements A-D, chapter XII
Assignment 7 (PDF) Griffiths, chapters 7, 8

Cohen-Tannoudji, chapter XI, Complements E, F, G
Assignment 8 (PDF) Griffiths, chapters 8, 10

Haxton, W. C. "The Solar Neutrino Problem." Annual Review of Astronomy and Astrophysics 33 (1995): 459-503.
Assignment 9 (PDF) Cohen-Tannoudji, chapter VIII

Griffiths, chapter 11

Ohanian, chapter 11
Assignment 10 (PDF) Cohen-Tannoudji, chapter VIII

Griffiths, chapters 9, 11

Ohanian, chapter 11



Optional Problem Set (PDF)




Projects

Special software is required to use some of the files in this section: .tex.



1) Project Summary

Everyone in 8.06 will be expected to research, write and "publish" a short paper on a topic related to the content of 8.05 or 8.06. The paper can explain a physical effect or further explicate ideas or problems covered in the courses. It can be based on the student's own calculations and/or library research. The paper should be written in the style and format of a brief journal article and should aim at an audience of 8.06 students.

Writing, editing, revising and "publishing" skills are an integral part of the project. Each of you will ask another student to edit your draft and will then prepare a final draft on the basis of the suggestions of your "peer editor". We will supply templates for the Revtex version of LaTeX (used by the Physical Review) so that you can prepare your paper in a finished, publishable form. We will also arrange a LaTeX tutorial, likely in place of sections one day in April.

You will submit your first draft marked up with editorial comments by your peer editor. This first draft will then be critiqued by a "writing assistant" (see below) and returned to you. Two weeks after the first draft is due, you will submit your final draft. Your papers will be graded on the intellectual quality of your work, the effectiveness of your presentation and the success of your prose style. A part of your grade will also be determined by how carefully and constructively you edited the draft of the paper for which you were the peer editor. The grade you earn for your paper will count 20% towards your final grade in 8.06.

Because 8.06 is a CI-M (Communication Intensive in the Major) Subject, in order to pass 8.06 you must obtain a grade of C or better on your term paper. If you do not succeed in this, you will get a grade of Incomplete until you revise your term paper sufficiently to earn at least a C, and only at that time you will be assigned a final grade, with your term paper grade counting 20%.

When a practicing physicist writes a research paper, he or she often asks a few colleagues to comment on a first draft. The final draft is then reviewed anonymously by one or several peers before it is accepted by a journal like the Physical Review. The goal of this informal and formal peer review process is to push authors to write papers which successfully communicate ideas among a community of peers. Your goal is to write a paper which presents a phenomenon or problem in quantum physics in a way which communicates your ideas clearly and effectively to your fellow 8.06 students, namely to your peers. Do not seek to teach Profs. Liu and Rajagopal, although they are always happy to learn. Do seek to teach your peers. If your peers cannot understand what you write, you have not succeeded. Note that writing for your peers is a much higher standard than writing for the faculty. Presenting a topic sufficiently clearly and logically that one of your peers new to this topic can learn about it requires clarity of thought and depth of understanding. These are the prerequisites for an effective written (or, for that matter, verbal) presentation.

We have obtained resources to support four "writing assistants" who can help you with writing, editing and preparing the paper. Each of you will be contacted by email by one of the writing assistants on March 29. (See the schedule below.) You should arrange to meet soon thereafter, and should seek their assistance from then on as you need it. They will critique the proposal and outline for your paper, and will also critique the first draft which you submit after it has been peer edited. In between, you may also ask them to help you with parts of your paper as you write them. Think of your writing assistant as a coach. They are there to help you, and are good at it. If you wish to get their help earlier than March 29, please submit your paper proposal and the name of your peer editor earlier, and one of the writing assistants will be assigned to help you.

By the time you turn in your final paper, it will have been edited by one of your peers and you will also have had time to implement the suggestions of one of the writing assistants. Past 8.06 students have found that their papers improve enormously through this process. Based on experience from previous years, by the time you turn in your finished paper, very many of you will have produced an account of a piece of physics written to a very high standard. It would be a shame if these papers were not "published". We shall have as our goal the "publication" of a journal consisting of all your papers. There are two important caveats: (i) only papers which are submitted electronically, using the LaTeX template provided, will be published; (ii) only papers which earn a grade of B or higher will be published. Subject to these caveats, we hope to produce a compilation of all of your papers. We will circulate this "journal" to all of you, so that you can in the end read the work of all your peers, and not just of the one person whose work you edited.



2) Schedule and Due Dates for the Paper

You should use the first part of the term to consider possible topics and to choose a peer editor. Your peer editor must be an 8.06 student, and must be someone whose own 8.06 paper topic is unrelated to yours. A list of suggested topics is given below, but you are free to choose topics not on this list upon first obtaining Prof. Rajagopal's approval. By the time Spring Break is upon us, you should have a good idea of what you are going to write about and should be well into the process of reading about your topic and doing the calculations, if any are involved. You should spend Spring Break completing your understanding of the physics that you plan to write about, completing any calculations that you plan, and outlining your paper. You will then be ready to write your proposal:

Your proposal is due on Tuesday March 29, in lecture. This must consist of: a title, a one paragraph description of what you plan to write about, an outline of your proposed paper, a list of several references you plan to use, the name of your peer editor, and your name and email address.

You will then be contacted by one of the writing assistants. They may either accept your proposal, or request that you revise it in response to their suggestions. You should arrange to meet with them as soon as possible (even if they accept your proposal). Anyone who has not met with their writing assistant at least once before submitting their first draft will be penalized.

Your peer edited first draft is due on Tuesday April 12 in lecture. This means that you must give your first draft to your peer editor several days earlier, to give that person sufficient time to critique it substantively by April 12. Each of you should then meet with your writing assistant by Friday April 15 in order to obtain their comments on your first draft. In fact, if A edits for B and B edits for A, I will make sure that A and B have the same writing assistant and would therefore suggest that you both meet him or her together, to obtain comments on both your papers simultaneously. You will get your first drafts back when you meet with your writing assistant.

A hard copy of your final, polished paper is due in lecture on Tuesday April 26. Think of this as submitting your paper to The 8.06 Physical Review. If you get back a positive report (i.e. grade of B or better) from the editor (Prof. Rajagopal) you will then be expected to submit your paper for publication electronically. You will all get a copy of the 2005 Physical Review.



3) Nature of the Paper

The aim of this project is to give a clear and pedagogical presentation of a "problem" or "phenomenon" in quantum mechanics.

A "problem" could be similar to but more elaborate than the type of problems that appear on problem sets. For example, coherent states were introduced briefly in the context of the harmonic oscillator in 8.05. A student might delve deeper into the coherent state formalism, describe the properties of coherent states, explain the types of problems where they are useful, and give some examples of their applications. Such a paper would resemble a short chapter in some hypothetical text book for 8.05. The principal references for a paper like this could be existing quantum mechanics texts and the references to the original literature to be found in them.



A paper focused on a "phenomenon" would introduce the phenonomenon and explain its origins in terms of the concepts and language of 8.06. For example, when we treated systems of identical particles at the end of 8.05 we alluded very briefly to the "allotropic forms of hydrogen" known as ortho and para hydrogen. A student might find out what they are, how their properties are understood in terms of Fermi-Dirac statistics, and describe the interesting role they played in the early history of quantum mechanics. Once again the principal references would likely be texts, perhaps modern physics texts in this case, histories of quantum physics, and the original literature.

Papers on "problems" might be based at least in part on your own calculations. Papers on "phenomena" might involve some library research. In either case reference must be given for any material taken from other sources. Do not plagiarize. Anyone who contemplates borrowing material directly from mainstream texts should consider how difficult it is to find a text that presents quantum physics at the level appropriate to 8.06.

We encourage students to write papers which expand upon a problem or phenomenon which was already introduced in either 8.05 or 8.06 lectures. If you do this, you should begin at the level of whatever we have already covered and then go farther. Students may also choose topics which have not appeared at all in class, but whose quantum mechanical explanation can be understood based upon what we have learned in 8.05 and 8.06.

Please do not try to choose subjects which are obscure, difficult or controversial. Misguided attempts like this to gain the respect of the faculty inevitably have the opposite effect. There are plenty of deep, interesting and challenging subjects in the mainstream of quantum mechanics.

Papers can range between 8 - 15 pages (in the LaTeX template provided) in length. These limits are firm.

Students are encouraged to use equations and figures to aid their presentation, much as they are used in articles and sophisticated textbooks.



4) Possible Topics

Students are welcome to suggest topics of their own. You should do this by sending Prof. Rajagopal a brief paragraph by email, summarizing the topic. There is no separate deadline by which you must do this, but note that your complete proposal is due on March 29. At the time you submit your proposal, you should already know that Prof. Rajagopal has approved your choice of topic. (Note that your writing assistant may nevertheless require you to revise your proposal.)

Here is a list of possible topics. In some cases, either Prof. Liu or Prof. Rajagopal will have ideas for where to begin reading about these topics. Not in all cases, however.

Coherent states.



The allotropic forms of hydrogen.



Nuclear Magnetic Resonance. For example, you might take off from where we stopped in 8.05 and explain how NMR is applied in a particular experimental context.



Magnetic monopoles, gauge invariance, and the Dirac quantization condition for the magnetic charge of a magnetic monopole.



Scattering off a magnetic flux tube.



Bell's theorem - can classical mechanics imitate quantum mechanics?



Neutrino oscillations in vacuum, beyond what we covered in 8.05.



Oscillation phenomena involving kaons and/or B mesons, beyond what we covered in 8.05.



The solar neutrino problem.



Levinson's theorem - how the scattering phase shift is related to the number of bound states in a potential.



The shell model of nuclear structure.



The properties of the deuteron.



The α-decay of 238 U.



The rotational and vibrational spectrum of diatomic molecules.



Dynamical SO(3) × SO(3) symmetry of the hydrogen atom.



Dynamical SU(n) symmetry of the harmonic oscillator in n-dimensions.



Supersymmetric quantum mechanics, beyond what we did in 8.05.



The Zeeman effect in weak, intermediate and strong magnetic fields.



The Lamb shift in hydrogen - evidence that relativistic quantum mechanics must be replaced by quantum field theory. (This is an example of a topic where you will not be able to give a complete derivation of the effect, but where those of you interested in the history of physics could write a paper which explains the quantum physics more qualitatively while at the same time describing the experiments and the history in full.)



The non-relativistic quark model of the proton, neutron and related particles.



Isospin - a quantum symmetry of elementary particles.



The 21 cm. line of hydrogen and its role in astrophysics.



The Casimir effect.



Feynman's path integral approach to quantum mechanics, and its application to several problems of your choice which we have previously analyzed using other methods (If you choose a formal topic like this, about a method rather than a phenomenon or problem, you must take it far enough to show how the method is applied to a phenomenon or problem.)



The van der Waals force between hydrogen atoms in excited states.



Quantum computing? (You may not write a paper that purports to be about "Quantum computing". You may only choose a topic within this area if you have a focussed idea, perhaps involving presentation of one of the ideas for implementation of a quantum computer, the quantum mechanics of the implementation, the difficulties, etc. Note also that you may not write a paper whose sole purpose is the presentation of Grover's and/or Shor's algorithms, since you will see those in lecture at the end of the semester.)



Quantum teleportation.



Quantum cryptography.



Bose-Einstein condensation.



Integer Quantum Hall Effect (There are a number of ways you could go beyond what we do in lecture.)



Landauer conductivity in two dimensional systems.



Photonic Crystals.



Quantum Dots.



The deHaas van Alphen effect as a tool for measuring the shapes of fermi surfaces in metals.



Periodic potentials and band structure.



An introduction to the quantum statistical mechanics of photons and the spectrum of black body radiation. (You could also include an account of how Planck was led to discover quantum mechanics in the first place, or of how the spectrum of black body radiation appears in the cosmic three degree background radiation.)



The density matrix formalism in quantum mechanics, and quantum statistical mechanics.



Optical pumping, masers, lasers.



Masers in astrophysics.



Interesting applications of the semiclassical approximation.



The Ramsauer-Townsend effect.



The Josephson effect.



The Wigner-Eckart theorem.



Fractional statistics in two dimensions.



Squeezed states and applications.



Wigner functions and applications.



Tunnelling, beyond the discussion in class. The Euclidean approach; effects of nonzero temperature.



The microscopic origin and effects of quantum dissipation, for example on tunnelling.



Inverse scattering method and its application to solitons.



5) Writing Tips

Here are some tips that you may find useful.

5.1) Structure

Identify a well-defined topic area as early as possible. Changing your focus is fine, but you may find that it requires substantial rewriting to keep things clear.



Work through and understand the physics before writing. You should do this over Spring Break. This will ensure that you have a well-defined topic before you start writing. You will find that this will make structuring the paper infinitely easier.



Make sure the main points of your paper are clearly indicated. This is especially important for scientific writing, since the reader can easily get bogged down in details. Your main points should be highlighted by the structure of the paper as well as mentioned in the introduction and/or abstract.



Write the abstract and, possibly, the introduction last.



After you have your outline ready, don't be afraid to draft later sections before earlier sections. If you understand the last half of your argument better than the first, start by writing the last half. Doing so will help you think through how to understand and explain the first half.

5.2) Style

In thinking about both style and structure, remember that you are writing a scientific paper and not a work of literature. The writing in great works of literature typically has multiple meanings, and can be understood in many ways, at different levels. It can be read differently by readers at different times or with different backgrounds. It often makes veiled allusions to other great literature. Over the years, great literature takes on meanings that go beyond those intended consciously by its author. In contrast, the central purpose of a scientific paper is the clear communication of your ideas to your readers, with no ambiguity, multiple meanings or veiled allusions. Your goal is to ensure that every one of your readers, who may indeed have varying backgrounds, understands your ideas in precisely the way that you intend. This means that clarity and precision are your paramount goals. You should seek to ensure that no reader can misunderstand what you intend to communicate in any sentence that you write, even should they willfully try to misunderstand you. To this end, write in simple, declarative sentences, avoid contorted constructions and always aim for clarity.



Feel free to use whichever voice you are most comfortable with. "I will show," "we will show" or "it will be shown" are all fine. For unknown reasons, some students seem to think that personal pronouns are banned and the passive voice is required. Nothing could be further from the truth. Good scientific writing should be animated and compelling. Your paper should "tell a physics story". I find the overuse of the passive voice to be deadening. Don't be dull. Clarity and precision come first, but don't fall into the trap of thinking that this can only be accomplished via boring your reader to tears. Not true.



Try to lead your reader along, motivating their interest, building up the physics ground work you need them to understand, drawing them into the story you are telling, and working up to a compelling conclusion.



All the advice I've given you about style is just as important when, later in life, you find yourself preparing a lecture or a seminar.

5.3) Some Details

Be rigorously consistent in your notation, even at the risk of being repetitive.



Clearly define every quantity that you introduce.



Avoid ambiguous references, such as "this shows". Instead, use references like "Eq. 4.1 shows." The LaTeX commands label and ef are useful here.



6) More on Peer Editing

As described in the project summary, each of you will act as an editor for one of your peers. (Note: if you cannot find someone to act as your editor, ask Prof. Rajagopal. He will pair people up as he gets such requests. You must list the name of your peer editor as part of your proposal, due on March 29.) When you finish your first draft, give it to your editor for editing. You must give your editor time to complete their work in time for you to submit your peer-edited first draft on Tuesday April 12.

As you are editing the work of one of your peers, you should start by praising what the document does well. If the author has made specific requests (i.e. "please see if my argument in this section makes sense to you") then spend much of your time responding to these specific requests. Do not focus on spelling and the mechanics of writing, unless asked by the author to do so. (Of course, note problems of this sort which you happen to spot, but this is not your main goal and the author should in general not rely on you for this sort of editorial review.) Instead, focus on helping the author to revise content, organization and logic. Do not just criticize. Make suggestions on how to solve the problems you notice in the paper.

As you edit the work of your peer, here are some of the questions which you should be thinking about:

What is the paper's main argument?



How interesting is it? Is the importance of the topic explained?



How specific is the argument? Would it benefit from being made more general or complete? Would it, in contrast, benefit from being made more focussed?



Is the paper divided into sections and subsections in a way which makes following its logic easy? Does each section flow logically from the preceding one? Do ideas flow smoothly from one paragraph to the next?



Early in the text, is there a clear road map of the entire document?



Are all outside sources documented? If, as will be the case for almost all 8.06 papers, the paper contains ideas which are not the results of calculations done by the author and are not ideas we have all seen in lecture, can you see from which source the author learned each such idea?



Are all technical terms which are new to you defined clearly, and used consistently?



If the paper presents the solution to a problem, what are the arguments on which the solution rests? Do you understand each argument and the solution as a whole? Is each part of each argument substantiated? (Either by calculation presented in the paper, or by reference to 8.05 and 8.06 material which you can see substantiates the argument.) Is there anything missing, which would help complete an argument?



If the paper describes a phenomenon, do you understand the description? Is the nature of the phenomenon clearly described? Are the reasons why the phenomenon is of interest clear? Do you understand the quantum mechanical explanation of the phenomenon presented by the author? What do you wish the author had included that would have given you a better understanding of the phenomenon?



7) The LaTeX Templates

LaTeX (and its ancestor TeX) are widely used in academic and technical publishing. They are "mark-up" languages, like HTML®, that tell a processor how to construct mathematical expressions that look like typeset text. One of the objectives of this assignment is to give you an experience preparing a physics paper for "publication". When practicing physicists submit papers to the Physical Review, they do so by emailing a LaTeX file, and perhaps some postscript figures, to the editorial office. If you wish to have your paper published, you will do the same.

Many 8.06 students have had previous exposure to LaTeX; some have not. Both to level the playing field and to make possible the publication of your finished papers, we will put a template on the web, for you to download. LaTeX itself is already available as standard MIT Server software.

The most computer-illiterate among you - nevertheless more literate than Professors Rajagopal and Liu by far - need only download the templates, open them in your favorite editor (such as emacs), and notice the way the LaTeX template deals with title pages, footnotes, references, equations, mathematical symbols in text and set off from text, equation labels, tabs, and so forth. You can construct your paper by cutting the text out of the template text and inserting your own.

In order for students to have access to all necessary macros, already installed on MIT Server, it may first be necessary to type: add newtex. [Note: this was necessary three years ago, but Prof. Rajagopal thinks it is now not necessary.]

You should begin by downloading the template, and making sure that you can LaTeX it successfully, to produce output which looks like the hard copy of the template paper which I will post on the server.

In order to do this, you will need the commands:

latex filename.tex will run the LaTeX typesetting program to produce typeset output from your input file. If there are errors in your LaTeX file, the file filename.log will contain error messages that are usually helpful. When LaTeX runs successfully, its output is filename.dvi, where dvi means "device independent". (Note that you will need to run LaTeX twice on the file, in order for all the references to bibliographic items and equation numbers to come out right.)



xdvi filename.dvi will display your output in its finished form.



dvips filename.dvi will convert the dvi file to a postscript file, send it to the printer, and then delete the postscript file. If, instead, you want to save a postscript file instead of printing it, use dvips -o filename.ps filename.dvi. This creates a postscript file named filename.ps. One reason to do this is that you can then view your output using ghostview (gv) instead of xdvi. gv is a more sophisticated viewer than xdvi. (A final note here: gv by default does not antialias to save time. It can be turned on and off from within gv or you can use the -antialias flag when calling gv to do it automatically.)

The template provided will contain postscript figures. If you know how to produce illustrations in postscript, the template will illustrate how to incorporate them into your paper. If you don't or don't want to bother, you are welcome to draw figures by hand or with your favorite graphics package, and simply staple them onto the end of your paper. Note, however, that if you wish to submit your final paper for publication, you must prepare it using the LaTeX template and must include any figures as encapsulated postscript files, as done in the template.

The template uses a macro called BoxedEPS in order to incorporate encapsulated postscript figures. This macro may be available on MIT Server, but to be safe we will make it available for you to download at the same time that you download the template itself.

We strongly urge people who are new at LaTeX to communicate with classmates. Likewise we strongly encourage LaTeX wizards to help the less experienced with the nuances of the language.



Sample Papers

8.06 Sample Term Paper (PDF)



Supporting Files

BoxedEPS (TEX)

Sample Paper (TEX)

Energy Levels (PDF)





Related Resources


Some Topics have a related experiment in the class 8.13-8.14: Experimental Physics I & II "Junior Lab," which is usually taken concurrently with Quantum Physics III.


Related resources table. LEC # TOPICS RELATED EXPERIMENTS
1 Natural Units  
2-4 Degenerate Fermi Systems  
4-8 Charged Particles in a Magnetic Field  
9-12 Time-independent Perturbation Theory Optical Emission Spectra of Hydrogenic Atoms

 

21-cm Radio Astrophysics

 

The Zeeman Effect

 

Optical Pumping of Rubidium Vapor

 

X-Ray Physics

 

Doppler-Free Laser Spectroscopy
13-15 Variational and Semi-classical Methods Superconductivity
16-18 The Adiabatic Approximation and Berry's Phase  
19-23 Scattering The Franck-Hertz Experiment

 

Rutherford Scattering
23-24 Time-dependent Perturbation Theory Optical Pumping of Rubidium Vapor

 

Doppler-Free Laser Spectroscopy
25 Quantum Computing Quantum Information Processing with NMR



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