Thermodynamics, Statistical Physics, and Quantum Mechanics

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5.63 Repulsive Square Well (Colorado)

Consider inthreedimensions a repulsive squarewell at theorigin

of width Thepotential is

A particle of energy is incidentupon the square well

(see FigureP.5.63).

a) Derive thephaseshift for

b) How does the phaseshiftbehave as

c) Derive thetotalcrosssection in the limit of zero energy.

5.64 3D Delta Function (Princeton)

Consider aparticle ofmass which scatters inthreedimension from a

potential which is ashell atradius

Derive the exact expression for thescatteringcrosssection in the
limit of verylow particleenergy.

QUANTUM MECHANICS