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Communication Dans Un Congrès Année : 2018

A conditionally integrable Schrödinger potential of a bi-confluent Heun class

Résumé

We present a bi-confluent Heun potential for the Schrödinger 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.

Dates et versions

hal-01758266 , version 1 (04-04-2018)

Identifiants

Citer

T.A. Ishkhanyan, A.M. Manukyan, A.M. Ishkhanyan. A conditionally integrable Schrödinger potential of a bi-confluent Heun class. 25th International Conference on Integrable Systems and Quantum Symmetries, Jun 2017, Prague, Czech Republic. pp.012019, ⟨10.1088/1742-6596/965/1/012019⟩. ⟨hal-01758266⟩
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