  In the existing literature various numerical techniques have been developed
to quantize the confined harmonic oscillator in higher dimensions. In obtaining
the energy eigenvalues, such methods often involve indirect approaches such as
searching for the roots of hypergeometric functions or numerically solving a
differential equation. In this paper, however, we derive an explicit matrix
representation for the Hamiltonian of a confined quantum harmonic oscillator in
higher dimensions, thus facilitating direct diagonalization.
