George Rawitscher
University of Connecticut, USA
Title: Revival of the phase-amplitude description of a quantum-mechanical wave function
Biography
Biography: George Rawitscher
Abstract
The Phase-Amplitude (Ph-A) description consists in writing the wave function as Ï•(r)), where y is the amplitude and Ï• the phase. Both functions vary slowly with the distance r, and hence should be easier to calculate than the highly oscillatory function . In 1930, W. E. Milne established the second order differential equation for y(r), which unfortunately is non-linear, and hence cumbersome to solve with the conventional finite difference methods. In 1962, M. J. Seaton and G. Peach demonstrated an iterative solution of Milne's equation, and in 2015 and 2016 the present author improved the iterative method by making use of a modern spectral expansion procedure of y(r) in terms of Chebyshev polynomials. The method is very economical and fast, as will be shown. One drawback of the iterative method is that it does not converge in the vicinity of the turning points. It is possible that this difficulty can be overcome by considering an alternative third order linear differential equation which may propagate the solution across the turning points. Attempts to solve this equation numerically will be described. If successful, that may represent an important advance for the Ph-A description.