Normalization of Certain Higher-Order Phase-Integral Approximations for Wavefunctions of Bound States in a Potential Well

Abstract

Furry has given a formula for the normalization integral of a physically acceptable solution of the time‐independent 1‐dimensional Schrödinger equation corresponding to a bound state. Considering the wavefunction of a bound state in a single‐well potential and using Furry's formula and the connection formulas discussed by N. Fröman, we derive the normalization factor for the higher‐order phase‐integral approximations introduced earlier by N. Fröman. For the special case of the first‐order JWKB approximation, the approximate normalization factor thus obtained is equivalent to that given by Pauli and Furry.