Simple Applications of Perturbation Theory

Abstract

A harmonic oscillator is an idealisation of actual mechanical systems. The real potential energy of particles is never represented by the function ½μω ²_o x² but by a much more complicated function U(x). The former expression is valid only when x is small. In order to make more precise the expression for the potential energy U(x) we can take into account, besides the term ½μω ²_o x², also higher terms in the expansion of U(x) in powers of the displacement x:

$$U\left( x \right) = {1 \over 2}\mu \omega _0^2{x^2} + \lambda {x^3} + \ldots .$$

(71.1)