1 / 16

Physics 452

Physics 452. Quantum mechanics II Winter 2011. Karine Chesnel. Phys 452. Homework. Today Mar 30 : assignment # 20 11.1, 11.2, 11.4 Friday Apr 1 : assignment #21 11.5, 11.6, 11.7. Sign up for the QM & Research presentations Next week, W April 6 or F April 8. Phys 452. Scattering.

scathy
Download Presentation

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 2011 Karine Chesnel

  2. Phys 452 Homework Today Mar 30: assignment # 20 11.1, 11.2, 11.4 Friday Apr 1: assignment #21 11.5, 11.6, 11.7 Sign up for the QM & Research presentations Next week, W April 6 or F April 8

  3. Phys 452 Scattering Relationship with cross-section Quantum treatment Spherical wave Plane wave

  4. Phys 452 Scattering Develop the solution in terms of spherical harmonics, Solution to Coulomb potential Radiation zone intermediate zone Scattering zone Partial wave analysis

  5. Phys 452 Scattering Rayleigh’s formula Scattered waves To be determined by solving the Schrödinger equation in the scattering region + boundary conditions Total cross-section for large r Partial wave analysis General solution where V~0: Wave function in spherical coordinates

  6. Phys 452 Scattering Boundary conditions Exploiting Total cross-section Partial wave analysis (Pb 11.3) Example: Hard-sphere scattering

  7. Phys 452 Assumption (low energy) Outside: Inside: Continuity of Boundary conditions at r = a Discontinuity of In spherical coordinates Find a relationship between a0, a and a... Scattering- Partial wave analysis Pb 11.4 Spherical delta function shell

  8. Phys 452 Scattering Physical representation in 1D Physical representation in 3D wall Phase - shifts

  9. Phys 452 Scattering wall interference Phase – shifts and interference effects Physical representation in 1D

  10. Phys 452 Quiz 32 In scattering and interference processes, the phase shift depends on the wavelength • True • False

  11. Phys 452 Scattering Outgoing spherical wave Incoming spherical wave If Phase - shifts Asymptotic behavior at If

  12. Phys 452 Scattering Connecting the asymptotic behavior at Partial wave amplitude Phase shift Phase - shifts

  13. Phys 452 Scattering Scattering amplitude Scattering Cross-section Phase - shifts

  14. Phys 452 Scattering – phase shift • In region 1 • In region 2 2) Continuity at boundary: 3) Identify the phase shift Pb 11.5 Reflection against a wall 1) Solve the Schrödinger equation wall Region 1 Region 2

  15. Phys 452 Scattering – Phase shift Boundary conditions We found Express the phase shift: using Express in terms of functions and Pb 11.6 Hard sphere scattering (Pb 11.3)

  16. Phys 452 Inside: Continuity of Boundary conditions Discontinuity of Express in terms of and Scattering- phase shifts Pb 11.7 Spherical delta function shell (Pb 11.4) Do NOT do the assumption Outside:

More Related