Related papers: On the quantum-mechanical singular harmonic oscillator

On the quantum-mechanical singular harmonic oscillator

URL: http://arxiv.org/abs/2112.03693v2
Date: Fri, 12 May 2023 17:29:51 GMT
Title: On the quantum-mechanical singular harmonic oscillator
Authors: Francisco M. Fern\'andez
Abstract summary: We obtain the eigenvalues and eigenfunctions of the singular harmonic oscillator $V(x)=alpha/ (2x2)+x2/2$ by means of the simple and straightforward Frobenius (power-series) method.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We obtain the eigenvalues and eigenfunctions of the singular harmonic oscillator $V(x)=\alpha/(2x^2)+x^2/2$ by means of the simple and straightforward Frobenius (power-series) method. From the behaviour of the eigenfunctions at origin we derive two branches for the eigenvalues for negative values of $\alpha$. We discuss the well known fact that there are square-integrable solutions only for some allowed discrete values of the energy.

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