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Date: 29-8-2016
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Phase Shift for Inverse Quadratic
A particle of mass m moves in one dimension in the right half-space (x > 0) with the potential
(i)
where the dimensionless constant determines the strength of the potential. Use WKB to calculate the phase shift as a function of energy.
SOLUTION
The turning point is C = λ/k. The phase integral is
The last integral is found in standard tables. To evaluate the phase shift, we need to evaluate this expression in the limit x → ∞, which gives kx – πλ/2. So the final expression for the phase shift is
(2)
The phase shift is independent of energy.
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