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Open Quantum Systems Decoherence

On the quantum-mechanical singular harmonic oscillator

arXiv
Authors: Francisco M. Fernández

Year

2021

Paper ID

40962

Status

Preprint

Abstract Read

~2 min

Abstract Words

64

Citations

N/A

Abstract

We obtain the eigenvalues and eigenfunctions of the singular harmonic oscillator V(x)=α/\(2x2\)+x2/2 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 α. 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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  • This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
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  • We obtain the eigenvalues and eigenfunctions of the singular harmonic oscillator V(x)=α/(2x^2)+x^2/2 by means of the simple and straightforward Frobenius (power-series) method.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2112.03693 [2] arXiv https://arxiv.org/abs/2112.03693 [3] Publisher https://arxiv.org/abs/2112.03693

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