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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.
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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 Relationship with cross-section Quantum treatment Spherical wave Plane wave
Phys 452 Scattering Develop the solution in terms of spherical harmonics, Solution to Coulomb potential Radiation zone intermediate zone Scattering zone Partial wave analysis
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
Phys 452 Scattering Boundary conditions Exploiting Total cross-section Partial wave analysis (Pb 11.3) Example: Hard-sphere scattering
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
Phys 452 Scattering Physical representation in 1D Physical representation in 3D wall Phase - shifts
Phys 452 Scattering wall interference Phase – shifts and interference effects Physical representation in 1D
Phys 452 Quiz 32 In scattering and interference processes, the phase shift depends on the wavelength • True • False
Phys 452 Scattering Outgoing spherical wave Incoming spherical wave If Phase - shifts Asymptotic behavior at If
Phys 452 Scattering Connecting the asymptotic behavior at Partial wave amplitude Phase shift Phase - shifts
Phys 452 Scattering Scattering amplitude Scattering Cross-section Phase - shifts
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
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)
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: