Evaluation of higher-order semiclassical phase integrals: Application of Chebyshev series approximation and Taylor series expansion

Abstract

A new approach for evaluating semiclassical phase integrals of the form ∮ dr f(r)/[E−U(r)]k+1/2 for any smooth potential U(r) is derived and tested. The new methods are based on a Chebyshev series or a Taylor series expansions of the integrand and do not explicitly involve handling weights required by existing forms of this procedure. In addition, they are much more flexible and easier to use and incorporate realistic error estimation.