A conditionally integrable Schr\"odinger potential of a bi-confluent Heun class
Quantum Physics
2018-02-23 v1
Abstract
We present a bi-confluent Heun potential for the Schr\"odinger equation involving inverse fractional powers and a repulsive centrifugal-barrier term the strength of which is fixed to a constant. This is an infinite potential well defined on the positive half-axis. Each of the fundamental solutions for this conditionally integrable potential is written as an irreducible linear combination of two Hermite functions of a shifted and scaled argument. We present the general solution of the problem, derive the exact energy spectrum equation and construct a highly accurate approximation for the bound-state energy levels.
Keywords
Cite
@article{arxiv.1802.07821,
title = {A conditionally integrable Schr\"odinger potential of a bi-confluent Heun class},
author = {T. A. Ishkhanyan and A. M. Manukyan and A. M. Ishkhanyan},
journal= {arXiv preprint arXiv:1802.07821},
year = {2018}
}