2013/04/01 by Douglas R.M. Pimentel, Douglas R. M. Pimentel, Pimentel, Douglas R. M. +2 · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mechanical and Optical Resonators #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.1304.0492
15 pages, 4 figures, in Portuguese
arxiv created 2013/04/01 · openalex publication_date 2013/04/01 · arxiv updated 2013/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The one-dimensional Schrödinger equation with the singular harmonic oscillator is investigated. The Hermiticity of the operators related to observable physical quantities is used as a criterion to show that the attractive or repulsive singular oscillator exhibits an infinite number of acceptable solutions provided the parameter responsible for the singularity is greater than a certain critical value, in disagreement with the literature. The problem for the whole line exhibits a two-fold degeneracy in the case of the singular oscillator, and the intrusion of additional solutions in the case of a nonsingular oscillator. Additionally, it is shown that the solution of the singular oscillator can not be obtained from the nonsingular oscillator via perturbation theory.