The JWKB Approximation

Abstract

The exact solution of the Schrödinger equation can be obtained only for a few potential energy variations. In this chapter we will develop a widely used approximate method which gives a direct solution of the one-dimensional Schrödinger equation

$$ \frac{{d^2 \psi }} {{dx^2 }} + k^2 (x)\psi (x) = 0 $$

((1))

where

$$ k^2 (x) = \frac{{2\mu }} {{\hbar ^2 }}\left[ {E - V(x)} \right] $$

((2))

Validity and other symbols have their usual meaning.

God is a mathematician of very high order and He used very advanced mathematics in constructing the universe.

P.A.M. Dirac ¹