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arXiv · 2309.00026

Spectral solutions for the Schr\"odinger equation with a regular singularity

Pushkar Mohile·Ayaz Ahmed·T. R. Vishnu·Pichai Ramadevi
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Abstract

We propose a modification in the Bethe-like ansatz to reproduce the hydrogen atom spectrum and the wave functions. Such a proposal provided a clue to attempt the exact quantization conditions (EQC) for the quantum periods associated with potentials V (x) which are singular at the origin. In a suitable limit of the parameters, the potential can be mapped to |x| potential. We validate our EQC proposition by numerically computing the Voros spectrum and matching it with the true spectrum for |x| potential. Thus we have given a route to obtain the spectral solution for the one dimensional Schr\"odinger equation involving potentials with regular singularity at the origin.

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Pushkar Mohile, Ayaz Ahmed, T. R. Vishnu, Pichai Ramadevi. 2023-08-31. Spectral solutions for the Schr\"odinger equation with a regular singularity. https://arxiv.org/abs/2309.00026

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