The isotropic bounded oscillators

We study the three-dimensional isotropic harmonic oscillator confined within spherical impenetrable walls. The potential in the box is of the harmonic oscillator type but outside the box the potential is infinite. The energy eigenvalues and some position expectation values are computed with great accuracy for different box sizes; our results are more accurate than previous calculations. By using the bounded harmonic oscillator wavefunctions as a basis set we obtain with the variational method the energy eigenvalues of a confined hydrogen atom.