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arXiv · 2112.03693

On the quantum-mechanical singular harmonic oscillator

Francisco M. Fernández
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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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Francisco M. Fernández. 2021-12-05. On the quantum-mechanical singular harmonic oscillator. https://arxiv.org/abs/2112.03693

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