1 / 14

Physics 452

Physics 452. Quantum mechanics II Winter 2012. Karine Chesnel. Phys 452. Homework. Friday Jan 20: Homework # 4 Pb 6.6, 6.8, 6.9, 6.10. Phys 452. Perturbation theory. Example of non-degenerate system Spring constant expansion in the harmonic oscillator. V. x. Phys 452. 3d. 2p. 2s.

shannonn
Télécharger la présentation

Physics 452

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. Physics 452 Quantum mechanics II Winter 2012 Karine Chesnel

  2. Phys 452 Homework Friday Jan 20: Homework # 4 Pb 6.6, 6.8, 6.9, 6.10

  3. Phys 452 Perturbation theory Example of non-degenerate system Spring constant expansion in the harmonic oscillator V x

  4. Phys 452 3d 2p 2s Atomic energy levels perturbation 1s Degenerateperturbation theory Example of degenerate system “lift the degeneracy”

  5. Phys 452 Quiz 5 Taking the electron spin into account, in how many energy levels, the (3d) band of Fe atom is susceptible to split, under the application of a magnetic field? A. 2 B. 3 C. 5 D. 6 E. 10

  6. Phys 452 are the eigenvalues of In fact, we are solving for Degenerate perturbation theory Two-fold degeneracy

  7. Phys 452 Degenerate perturbation theory Two-fold degeneracy E d=2 E0

  8. Phys 452 If Then, using Choose a “good” clever basis (to make W diagonal) Degenerate perturbation theory Two-fold degeneracy In fact, we are solving for Pb 6.6

  9. Phys 452 Find eigenvalues of 3 energies Find eigenvalues of N energies Try to find a “good” basis to make W diagonal Degenerate perturbation theory Higher –order degeneracy d = 3 d = N Pb 6.10

  10. Phys 452 • Start with an ortho-normal basis of the unperturbed states • If the state is non-degenerate: • If the state is degenerate: build • Diagonalize W : the eigenvalues are l Degenerate perturbation theory General method Pb 6.8 & 6.9

  11. Phys 452 Quiz 5b Here is a list of energy levels for a given system (V,5V,3V,3V,2V, 3V,5V,5V,V,7V) How many levels are degenerate and non-degenerate? A. (3,1) B. (2,3) C. (3,2) D. (1,4) E. (4,1)

  12. Phys 452 Perturbation: in a sub-cell Build W for the first excited state Diagonalize W l Degenerate perturbation theory Example: cubic infinite square well z y x

  13. Phys 452 Perturbation: ? • Build W for the first excited state ? ? l Degenerate perturbation theory Example: problem 6.8 z y x • Diagonalize W

  14. Phys 452 Degenerate perturbation theory Problem 6.9 e is the pertubation • Identify the unperturbed states • determine which one are degenerate or non degenerate • Find the exact solution of the perturbed Hamiltonian • Compare with the first order correction • Use W for degenerate state • Compare with the second order correction for non- degenerate states

More Related