Spectral solutions for the Schr\"odinger equation with a regular singularity
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.
Keywords
Cite
@article{arxiv.2309.00026,
title = {Spectral solutions for the Schr\"odinger equation with a regular singularity},
author = {Pushkar Mohile and Ayaz Ahmed and T. R. Vishnu and Pichai Ramadevi},
journal= {arXiv preprint arXiv:2309.00026},
year = {2023}
}
Comments
26 pages, 6 figures, 5 tables; A mathematica file is attached as an ancillary file; some typos corrected and reference added in v2