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