The bound-state solutions of the one-dimensional pseudoharmonic
oscillator
The bound-state solutions of the one-dimensional pseudoharmonic
oscillator
We study the bound states of a quantum mechanical system consisting of a simple harmonic oscillator with an inverse square interaction, whose interaction strength is governed by a constant $\alpha$. The singular form of this potential has doubly-degenerate bound states for $-1/4\leq\alpha<0$ and $\alpha>0$; since the potential is symmetric, these …