Next we solve for the energy eigenstates of the
harmonic oscillator
potential
,
where we have eliminated the spring constant
by using the classical
oscillator frequency
.
The energy eigenvalues are

The energy eigenstates turn out to be a polynomial (in ) of degree times . So the ground state, properly normalized, is just

We will later return the harmonic oscillator to solve the problem by operator methods.

Jim Branson 2013-04-22