Thermodynamics, Statistical Physics, and Quantum Mechanics

QUANTUM MECHANICS 311

The factor is thephase changewhen the particle goesthrough the

turning point where

For the present problem we have that for and this part

of the integral exactly cancels the term For the potential is

assumingthat The turning point is so we

have

5.59 Parabolic Phase Shift (Tennessee)

Again we use(S.5.58.1) forthe phase shift. Thepotential in the

present problem is zero for The integral in this region cancels the

term To the left of the origin, the turning point is

The integral over again equals The phase shift is linear with
energy and has a constant term.

5.60 Phase Shift for Inverse Quadratic (Tennessee)

Again we use (S.5.58.1) for the phase shift. The turning point is
The phase integral is