Uniform Solutions for Scattering by a Potential Barrier and Bound States of a Potential Well

摘要

The one dimensional Schrodinger equation is solved asymptotically for scattering of a particle by a potential barrier and for bound states of a potential well, when the potentials change little in a wavelength. Both solutions are represented uniformly in space, rather than nonuniformly as in the WKB method. This avoids matching expansions and using connection formulas. The scattering solution and the complex reflection and transmission coefficients are also uniform in the particle energy.