The 1-dimensional confined harmonic oscillator revisited

Abstract

We study the size effect on the energy levels of the1–dimensional harmonic oscillator confined within a box of with impenetrable walls and large L. We use the particle in a box basis set to diagonalize the Hamiltonian of the confined harmonic oscillator. In this way we obtain theenergy eigenvalues and eigenfunctions as a functions of L. We compare our numerical results with those reported in literature finding goodagreement with the exact ones.