© Daniel Kleppner.

The ground state wavefunction for the harmonic oscillator, found by solving Schrödinger's equation, is shown on the left. The square of the wave function, defined as the amplitude of the wave function multiplied by itself at every point, is shown on the right. The square of the wavefunction is the probability distribution that gives the probability of finding a particle in a harmonic oscillator ground state at any position in space. The harmonic oscillator is one of the few systems for which an exact solution is possible. However, powerful analytical techniques, and powerful computers, have made it possible to solve Schrödinger's equation for a wide variety of systems. (Unit: 5)