Quantization of Liénard's nonlinear harmonic oscillator and its solutions in the framework of supersymmetric quantum mechanics
arXiv:1911.11871 · doi:10.1088/1402-4896/aaec4f
Abstract
Liénard-type nonlinear one-dimensional oscillator is quantized using van Roos symmetric ordering recipe for the kinetic-like part of the new derived Hamiltonian. The corresponding Schrödinger equation is exactly solved in momuntum space via the approach of supersymmetric quantum mechanics (SUSYQM). The bound-states energy spectra and corresponding wave functions are given explicitly in terms of the ambiguity parameters. The limiting case of no deformation agrees exactly with the eigenenergies and eigenfunctions of the ordinary quantum harmonic oscillator.
14 pages, no figures