Open AccessCoherent states for rational extensions and ladder operators related to infinite-dimensional representations
Author(s) -
Scott E. Hoffmann,
Véronique Hussin,
Ian Marquette,
Yao-Zhong Zhang
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1416/1/012013
Subject(s) - creation and annihilation operators , hermite polynomials , harmonic oscillator , laguerre polynomials , eigenvalues and eigenvectors , ladder operator , mathematics , coherent states , wave function , rational function , quantum harmonic oscillator , polynomial , pure mathematics , algebra over a field , extension (predicate logic) , quantum mechanics , mathematical analysis , physics , quantum , compact operator , computer science , programming language
The systems we consider are rational extensions of the harmonic oscillator, the truncated oscillator and the radial oscillator. The wavefunctions for the extended states involve exceptional Hermite polynomials for the oscillator and truncated oscillator and exceptional Laguerre polynomials for the radial oscillator. In all cases it is possible to construct ladder operators that have infinite-dimensional representations of their polynomial Heisenberg algebras and couple all levels of the systems. We construct Barut-Girardello coherent states in all cases, eigenvectors of the respective annihilation operators with complex eigenvalues. Then we calculate their physical properties to look for classical or non-classical behaviour.