PHYS264 spring 2010 page 1 PHYS264-Scattering and Transport Thursday 4. March 2010 Topic: Wave Scattering Partial Waves Comment: Some points to be added.

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PHYS264 spring 2010 page 1 PHYS264-Scattering and Transport Thursday 4. March 2010 Topic: Wave Scattering Partial Waves Comment: Some points to be added

PHYS264 spring 2010 page 2 Partial wave method is based on 1. Transformation to spherical coordinates Most suitable for radial (spherically symmetric) forces/potentials 2. Separation o variables r,  3. Expansion on a set of orthogonal functions Topics – expansions, separation of variables, radial equation … Legendre functions, spherical harmonics All are conveniently listed in wikipedia

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PHYS264 spring 2010 page 11 From PHYS208 – and 1995 Matlab Conference Paper - with Dirac notation This is how operators become matrices And the functions (states) become Column vectors

PHYS264 spring 2010 page 12 From PHYS208 – and 1995 Matlab Conference Paper - with Dirac notation

PHYS264 spring 2010 page 13 Euclidean three-dimensional space analogy; with Dirac notation

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