Degeneracy of 1D-Harmonic oscillator Biswanath Rath

Degeneracy

Abstract

Eigenstates of a quantum mechanical system reflect one to one correspondence with energy level. However, in some systems more than one or a group of eigenstates correspond to a single eigenvalue. In order to introduce more than one eigenstate corresponding to single energy eigenvalue in 1D-harmonic oscillator, we introduce a new perturbation term and find entire eigenspectrum become degenerate in nature without changing the eigenfunctions of the system.