In quantum physics, you can find the wave function of the ground state of a quantum oscillator, such as the one shown in the figure, which takes the shape of a gaussian curve.
The ground state of a quantum mechanical harmonic oscillator.
As a gaussian curve, the ground state of a quantum oscillator is
How can you figure out A? Wave functions must be normalized, so the following has to be true:
Substituting for
gives you this next equation:
You can evaluate this integral to be
Therefore,
This means that the wave function for the ground state of a quantum mechanical harmonic oscillator is
Cool. Now you’ve got an exact wave function.
