Degeneracy in one-dimensional quantum mechanics: A case study

摘要

In this work we study the isotonic oscillator, V(x) = Ax~2 + Bx~(-2), on the whole line -∞ < x < +∞ as an example of a one-dimensional quantum system with energy level degeneracy. A symmetric double-well potential with a finite barrier is introduced to study the behavior of energy pattern between both limit: the harmonic oscillator (i.e., a system without degeneracy) and the isotonic oscillator (i.e., a system with degeneracy).