Isospectral mapping for quantum systems with energy point spectra to polynomial quantum harmonic oscillators
View/ Open
Author
Steuernagel, Ole
Klimov, Andrei
Attention
2299/24205
Abstract
We show that a polynomial Hˆ(N) of degree N of a harmonic oscillator hamiltonian allows us to devise a fully solvable continuous quantum system for which the first N discrete energy eigenvalues can be chosen at will. In general such a choice leads to a re-ordering of the associated energy eigenfunctions of Hˆ such that the number of their nodes does not increase monotonically with increasing level number. Systems Hˆ have certain ‘universal’ features, we study their basic behaviours.