The Variational Method and the Harmonic Oscillator

Abstract

Frankly speaking, we didn’t really solve the Schrödinger equation for the particle in a box. We displayed a solution and showed that it worked. In fact, there are very few Schrodinger equations for which one can find solutions in the form of simple analytical functions. It is necessary to resort to approximate techniques. The most important of these is the variational method, which we will discuss in this chapter. Its use will be illustrated by applying it to problems for which exact solutions in the form of analytical functions can be found. These will be the particle in the box and the harmonic oscillator. The latter problem is of great importance and its solutions will be studied in some detail.

“I can see you’re trying to invent something.”