David J. Fernández C, VS Morales-Salgado
Published 2013-10-21, updated 2013-12-09Version 3
Supersymmetry transformations of first and second order are used to generate Hamiltonians with known spectra departing from the harmonic oscillator with an infinite potential barrier. It is studied also the way in which the eigenfunctions of the initial Hamiltonian are transformed. The first and certain second order supersymmetric partners of the initial Hamiltonian possess third-order differential ladder operators. Since systems with this kind of operators are linked with the Painlev\'e IV equation, several solutions of this non-linear second-order differential equation will be simply found.
Some Properties of an Infinite Family of Deformations of the Harmonic Oscillator
MHD alpha^2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
Quantum counterparts of VII$_{a}$, III$_{a=1}$, VI$_{a\neq1}$ over harmonic oscillator
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