Exact diagonalization of the $d-$dimensional confined quantum harmonic   oscillator
  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. 
Kunle Adegoke, Adenike Olatinwo, Henry Otobrise, Funmi Akintujoye and   Afees Tiamiyu
quant-ph math-ph math.MP