The confined N-dimensional harmonic oscillator revisited

In a recent work, Al-Jaber (2008 Int. J. Theor. Phys. 47 1853) calculated the energy eigenvalues of a confined N-dimensional harmonic oscillator. He also examined the correlation between the energy eigenvalues of harmonic oscillators in different dimensions. In the present work, we improve the energy eigenvalues obtained by Al-Jaber. In particular, we study the size effects on the energies of the ground and a few excited states of the N-dimensional (N=1-5 and N=10), isotropic harmonic oscillator confined within an impenetrable hypersphere of radius rc. The numerical results obtained are the most accurate reported to date, with the ground state values reported to 50 decimal places. Our eigenvalues are compared to those published previously. As a counterpart to Al-Jaber's work, we also report radial expectation values, dipole transition moments and dipole polarizabilities for N=1-3 as a function of rc.