Perturbative analysis as applied to the WKB method

Abstract

The differential equation of the from (av)' + f(v) = 0, where a, v, and f are functions of x. Solutions for v(x) are found for f < 0, f = 0, and f > 0. The results are applied to the time-independent Schrondinger equation for a particle of varying mass. A Mathematica program is created to solve the Schrodinger Equation and the corresponding eigenvalues are obtained for any potential V which decreases, reaches a minimum and increases. Thus, the resulting eigenfunctions are found.