Mathematical Physics


Regular and Singular Rational Extensions of the Harmonic Oscillator with Two Known Eigenstates

Authors: Spiros Konstantogiannis

Exactly solvable rational extensions of the harmonic oscillator have been constructed as supersymmetric partner potentials of the harmonic oscillator [1] as well as using the so-called prepotential approach [2]. In this work, we use the factorization property of the energy eigenfunctions of the harmonic oscillator and a simple integrability condition to construct and examine series of regular and singular rational extensions of the harmonic oscillator with two known eigenstates, one of which is the ground state. Special emphasis is given to the interrelation between the special zeros of the wave function, the poles of the potential, and the excitation of the non-ground state. In the last section, we analyze specific examples.

Comments: 50 Pages.

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Submission history

[v1] 2017-08-15 06:49:15

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