1 / 64

Course Name: Quantum Mechanics ( 量子力學 ) Part II Applications Report : C. K. Lee

Course Name: Quantum Mechanics ( 量子力學 ) Part II Applications Report : C. K. Lee Major References: 1. J. G. David, 2005, “Introduction to Quantum Mechanics”, Pearson Prentice Hall.

maddox
Download Presentation

Course Name: Quantum Mechanics ( 量子力學 ) Part II Applications Report : C. K. Lee

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Course Name:Quantum Mechanics (量子力學) Part II Applications Report :C. K. Lee Major References: 1. J. G. David, 2005, “Introduction to Quantum Mechanics”, Pearson Prentice Hall. 2. P. W. Atkins, 1998, “Physical Chemistry”, Oxford University Press. Course Outline: 國立中正大學 • Scattering ☺☺ • The adiabatic approximation ☺☺ • Time-dependent perturbation theory ☺☺ • The WKB approximation ☺☺ • The variational principle ☺

  2. Classical scattering theory 2-D

  3. 3-D

  4. Example: Hard-sphere scattering

  5. Rutherford scattering In order to find out more about the structure of the atom. Ernest Rutherford fired alpha particles at a thin sheet of gold foil. Alpha particles have a positive charge and so does the nucleus of a gold atom, hence they repel each other and the alpha particles are scattered when they pass close by. The alpha particles produce a tiny spark of light when they hit a fluorescent screen which can then be detected. The apparatus Rutherford used looked like this: References by [http://www.waowen.screaming.net/revision/nuclear/rsanim.htm]

  6. Quantum scattering theory

  7. 3-D

  8. Partial wave analysis I. II. combine

  9. Partial wave amplitudes

  10. Phase shifts I. II.

  11. Adiabatic Processes

  12. The adiabatic approximation

  13. Geometric phase

  14. Quantum Interference

  15. The Aharonov-Bohn Effect In 1959 Y. Aharanov and D. Bohm demonstrated that the vector potential had more physical significance that had been previously thought. They have us imagine sending electrons past a long, tightly wound solenoid that has been running for a long time.

  16. Other Applications Junichiro Kono及其在萊斯大學及佛羅里達州州立大學的研究伙伴將單璧式半導體碳奈米管的溶液置於45 Tesla的強磁場中,並觀察其吸收與發射光譜,結果發現其導電帶與共價帶之間的能隙隨磁場的增加而變窄。 References: J. Kono et at. “Optical Signatures of the Aharonov-Bohm Phase in Single-Walled Carbon Nanotubes,” Science 21 May 2004:Vol. 304. no. 5674, pp. 1129 – 1131 伊利諾州大學香檳校區的Alexey Bezryadin等人也發現,原本沒有能隙的金屬型複壁式碳奈米管,在外加磁場下能隙會逐漸打開變寬,碳管因而呈半導體性;然而持續升高磁場,能隙卻又降為零而回歸金屬性。 References: A. Bezryadin et al. “h/e Magnetic Flux Modulation of the Energy Gap in Nanotube Quantum Dots ,“ Science 21 May 2004:Vol. 304. no. 5674, pp. 1132 - 1134 以上這些效應以往從未在奈米管上被觀測到,但它們都符合理論預測,而且由此突顯了的量子力學A-B效應的重要性。A-B效應雖然已在許多系統(包括碳奈米管)中出現過,但這卻是首度發現它能影響固體的能帶結構。

  17. Time dependent part Total Hamiltonian Time independent part Time-dependent perturbation theory

  18. Ex: Two-level systems

  19. absorption and Emission of radiation atom photon

  20. Ex: Laser (light amplification by stimulated emission of radiation)

  21. Spontaneous Emission Einstein’s A & B coefficient Spontaneous Emission Stimulated Emission Absorption

  22. Blackbody spectrum, giving the energy per unit volume, per unit frequency, for an electromagnetic field in equilibrium at temperature T.

  23. Selection Rules

  24. The WKB approximation

  25. Classical region

  26. Example for Classical region

  27. Nonclassical (tunneling) region

  28. Gamow’s theory of alpha decay An alpha particle contain Two protons & neutrons

  29. The connection formulas

  30. Patching wave function

  31. Connection formulas

  32. The variational principle The variational principle will get you an upper bound for Egs, which is sometimes all you need, and often, if you’re clever about it, very close to the exact value. Pick any normalized function whatsoever; I claim that Solving procedures: 1) Suggest trial wave function 2) Determine a coefficient by normalization 3) Obtain the expectation values of Hby inner-product notation 4) Differential of <H> to obtain another coefficient

  33. Example 1

  34. The harmonic oscillator Refer to Part I Theory

More Related