University of Connecticut

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Atomic, Molecular, and Optical Physics Seminar

Monday, November 2, 2015
4:00pm – 5:00pm

Storrs Campus
Gant Science Complex, Physics, Room PB-121

Professor George Rawitscher, of the UConn Physics Department

“The Phase Amplitude Representation of a Wave Function in the Classically Forbidden Region”

In the classically forbidden region, where the potential V is larger than the energy E, the solution of the Schroedinger Eq. increases or decreases exponentially, but is non-oscillatory. The phase amplitude method (Ph-A) is also applicable to this region, and provides again an extension of the WKB approximation. It is shown how to solve Milne's non-linear equation for the amplitude "y" by an iterative method based on the work of Seaton and Peach (1962), and from there obtain the Phase. However, the iterations do not converge as well as for the case when V is less than the energy E, and the radial region where convergence occurs does not extend as far as the turning points. The accuracy reached is at least a factor of 10 larger than that that of the WKB, as will be demonstrated for a Morse- type potential. The Ph-A method is most useful for a resonant case, where the wave function in the barrier region decreases with distance, and where the errors of the solution by means of a finite difference method are largest.


Dawn Rawlinson, 486-4916,

Physics Department (primary)

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