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

Ole Steuernagel; Andrei Klimov

doi:10.1016/j.physleta.2021.127144

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

Ole Steuernagel
, Andrei Klimov

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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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 language	English
Article number	127144
Number of pages	5
Journal	Physics Letters A
Volume	392
Early online date	9 Jan 2021
DOIs	https://doi.org/10.1016/j.physleta.2021.127144
Publication status	Published - 15 Mar 2021

Keywords

quant-ph

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2020_PolyKerr_Andrei
© 2021 Elsevier B.V. All rights reserved. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1016/j.physleta.2021.127144
Accepted author manuscript, 1.63 MBLicence: CC BY-NC-ND

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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 {\textquoteleft}universal{\textquoteright} features, we study their basic behaviours. ",

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N2 - 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.

AB - 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.

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JO - Physics Letters A

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

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