2013/10/31 by David J. Fernández C, VS Morales-Salgado · 2 citations
Mathematics · Physics and Astronomy · #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8113/47/3/035304
published as J. Phys. A 47 (2014) 035304
arxiv created 2013/12/09 · arxiv updated 2016/12/12
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 Painlevé IV equation, several solutions of this non-linear second-order differential equation will be simply found.