The W.B.K. Method

Abstract

It is interesting to realize that the old Sommerfeld-Wilson-Ishiwara quantization method (Sect. 1.7) gives in many cases of physical interest values for the energy levels very close to those one would obtain after solving the Schrödinger equation exactly.This fact was explained after Wentzel [WE 26], and almost simultaneously and independently, Brillouin [BR 26] proposed an approximation method to solve the Schrödinger equation based on mathematical techniques developed by Jeffreys [JE 24]. This method was later improved by Kramers [KR 26], and it is commonly known as the W.B.K. method or semiclassical approximation. It provides a procedure to compute approximately energy levels and eigenfunctions which complements, sometimes with great efficiency, more general computational methods that will be introduced in later chapters.