The 1-dimensional confined harmonic oscillator revisited

Abstract

We study the size effect on the energy levels of the $1$--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 the energy eigenvalues and eigenfunctions as a functions of $L$. We compare our numerical results with those reported in literature finding good agreement with the exact ones.