Because the three-dimensional harmonic oscillator potential (Equation 4.188) is spherica...

Because the three-dimensional harmonic oscillator potential (Equation 4.188) is spherically symmetric, the Schrodinger equation can be handled by separation of variables in spherical coordinates, as well as cartesian coordinates. Use the power series method to solve the radial equation. Find the recursion formula for the coefficients, and determine the allowed energies. Check your answer against Equation 4.189.