Bound State Energies Using Phase Integral Methods
Authors: R. B. White
Abstract: The study of asymptotic properties of solutions
to differential equations has a long and arduous history, with the
most significant advances having been made in the development of
quantum mechanics. A very powerful method of analysis is that of
Phase Integrals, primarly due to Heading. Key to this analysis are
the Stokes constants and the rules for analytic continuation of an
asymptotic solution through the complex plane. These constants are
easily determined for isolated singular points, by analytically
continuing around them and, in the case of analytic functions,
requiring the asymptotic solution to be single valued. However,
most interesting problems of mathematical physics involve several
singular points. By examination of bound state problems involving
multiple singular points, we show that the method of Phase
Integrals can greatly improve the determination of bound state
energy over the simple WKB values.
Submitted to: Communications in Nonlinear Science and Numerical Simulation
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