Degeneracy in one‐dimensional quantum mechanics: A case study

In this work we study the isotonic oscillator, V(x) = Ax 2 + Bx −2 ,o n 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). © 2009 Wiley Periodicals, Inc. Int J Quantum Chem 110: 1317-1321, 2010