TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.7.3.041
TI  - Spectral solutions for the Schrödinger equation with a regular singularity
PY  - 2024/07/05
UR  - https://scipost.org/SciPostPhysCore.7.3.041
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 7
IS  - 3
SP  - 041
A1  - Mohile, Pushkar
AU  - Ahmed, Ayaz
AU  - Vishnu, T. R.
AU  - Pichai, Ramadevi
AB  - 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 condition (EQC) for the quantum periods associated with potentials $V(x)$ which are of the form $(V(x) = |x| + a/|x| + b/|x|^2 )$. We validate the EQC proposal by showing that our computed Voros spectrum in the limit $a,b → 0$ is matching well with the true spectrum of the familiar $|x|$ potential. Thus we have given a route to obtain the spectral solution for the one dimensional Schrödinger equation involving potentials with regular singularity at the origin.
ER  -

@Article{10.21468/SciPostPhysCore.7.3.041,
	title={{Spectral solutions for the Schrödinger equation with a regular singularity}},
	author={Pushkar Mohile and Ayaz Ahmed and T. R. Vishnu and Pichai Ramadevi},
	journal={SciPost Phys. Core},
	volume={7},
	pages={041},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.7.3.041},
	url={https://scipost.org/10.21468/SciPostPhysCore.7.3.041},
}