Open AccessLinearised coherent states for non-rational SUSY extensions of the harmonic oscillator
Author(s) -
Alonso ContrerasAstorga,
David Fernández,
César Muro-Cabral
Publication year - 2022
Publication title -
acta polytechnica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.207
H-Index - 15
eISSN - 1805-2363
pISSN - 1210-2709
DOI - 10.14311/ap.2022.62.0030
Subject(s) - coherent states , ladder operator , harmonic oscillator , supersymmetry , operator (biology) , eigenvalues and eigenvectors , quantum harmonic oscillator , completeness (order theory) , mathematics , quantum , operator product expansion , creation and annihilation operators , quantum mechanics , pure mathematics , mathematical physics , physics , mathematical analysis , extension (predicate logic) , compact operator , computer science , biochemistry , chemistry , repressor , transcription factor , gene , programming language
In this work, we derive two equivalent non-rational extensions of the quantum harmonic oscillator using two different supersymmetric transformations. For these extensions, we built ladder operators as the product of the intertwining operators related with these equivalent supersymmetric transformations, which results in two-step ladder operators. We linearised these operators to obtain operators of the same nature that follow a linear commutation relation. After the linearisation, we derive coherent states as eigenstates of the annigilation operator and analyse some relevant mathematical and physical properties, such as the completeness relation, mean-energy values, temporal stability, time evolution of the probability densities, and Wigner distributions. From these properties, we conclude that these coherent states present both classical and quantum behaviour.