2016/04/05 by Kunle Adegoke, Adegoke, Kunle, Adenike Olatinwo +7 · 1 citation
Mathematics · Physics and Astronomy · #Gyrotron and Vacuum Electronics Research #Mechanical and Optical Resonators #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1604.01095
arxiv created 2016/04/21 · arxiv updated 2016/04/22
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.