Isospectral mapping for quantum systems with energy point spectra to polynomial quantum harmonic oscillators

Ole Steuernagel, Andrei Klimov

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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.
Original languageEnglish
Article number127144
Number of pages5
JournalPhysics Letters A
Volume392
Early online date9 Jan 2021
DOIs
Publication statusPublished - 15 Mar 2021

Keywords

  • quant-ph

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