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

• URL: http://arxiv.org/abs/2309.00026v2
• Date: Tue, 12 Sep 2023 22:50:03 GMT
• Title: Spectral solutions for the Schr\"odinger equation with a regular singularity
• Authors: Pushkar Mohile, Ayaz Ahmed, T.R.Vishnu, Pichai Ramadevi
• Abstract summary: We attempt the exact quantization conditions (EQC) for the quantum periods associated with potentials V (x) which are singular at the origin. We validate our EQC proposition by numerically computing the Voros spectrum and matching it with the true spectrum for |x| potential. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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