A conditionally exactly solvable generalization of the potential step

2015/12/14 by A. López-Ortega, Lopez-Ortega, A. · 1 citation
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Experimental and Theoretical Physics Studies #Quantum and Classical Electrodynamics

paper · pdf · doi:10.48550/arxiv.1512.04196

Abstract

Motivated by the interest in non-relativistic quantum mechanics for determining exact solutions to the Schrodinger equation we give two potentials that are conditionally exactly solvable. The two potentials are partner potentials and we obtain that each linearly independent solution of the Schrodinger equation includes two hypergeometric functions. Furthermore we calculate their reflection and transmission amplitudes. Finally we discuss some additional properties of these potentials.

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