2010/02/06 by M. Reyes, Marco A. Reyes, Reyes, Marco A. +3
Mathematics · Physics and Astronomy · #Photorefractive and Nonlinear Optics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #math-ph #math.MP #msc:70B05
paper · pdf · doi:10.48550/arxiv.1002.1344
arxiv created 2010/02/06 · arxiv updated 2010/02/26
We propose an alternative factorization for the simple harmonic oscillator hamiltonian which includes Mielnik's isospectral factorization as a particular case. This factorization is realized in two non-mutually adjoint operators whose inverse product, in the simplest case, lead to a new Sturm-Liouville eigenvalue equation which includes Schrodinger's equation for the oscillator and Hermite's equation as particular cases for limiting values of the factorization's parameter, and whose eigenfunctions allow us to define new generalized Hermite functions.