Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:math-ph/0310015 · Journal of Physics A Mathematical and General

An algebraicq-deformed form for shape-invariant systems

A N F Aleixo, A. B. Balantekin, M A Cândido Ribeiro

Published Nov 4, 2003• 21 citations
arXivHTMLPDF

Abstract

A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q -deformed ladder operators. We show that these new ladder operators satisfy new q -deformed commutation relations. In this context we construct an alternative q -deformed model that preserves the shape-invariance property presented by the primary system. q -deformed generalizations of Morse, Scarf and Coulomb potentials are given as examples.

DOI
10.1088/0305-4470/36/46/007

Related papers

Multiparameter deformation theory for quantum confined systems

A N F Aleixo, A. B. Balantekin

We introduce a generalized multiparameter deformation theory applicable to all supersymmetric and shape-invariant systems. Taking particular choices for the deformation factors used in the construction of the deformed ladder operators, we show that we can generalize the one-parameter quantum-deformed harmonic oscillator models and build alternative multiparameter deformed models that are also shape invariant like the primary undeformed system.

Journal of Mathematical Physics•Nov 1, 2009•13 citations

Purely squeezed states for quantum deformed systems

A N F Aleixo, A. B. Balantekin

The generalized purely squeezed states for primary shape-invariant potentials systems, quantum deformed by different models, are constructed by the ladder-operator method within an algebraic approach based on supersymmetric quantum mechanics. The characteristic properties of these states as well as their quantum statistical properties and squeezing effects for generalized quadrature observables are studied and analyzed in terms of the quantum deformation parameter q. An application is given for a quantum deformed Pöschl–Teller potential system, and numerical results are presented and discussed in detail.

Journal of Mathematical Physics•Jun 1, 2008•5 citations

Generalized Ladder Operators for Shape-invariant Potentials

Elso Drigo Filho, M A Cândido Ribeiro

A general form for ladder operators is used to construct a method to solve bound-state Schrödinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the elegance and the utility of the method we use it to obtain energy spectra and eigenfunctions for the one-dimensional harmonic oscillator and Morse potentials and for the radial harmonic oscillator and Coulomb potentials.

arXiv:nucl-th/0108073•Physica Scripta•Jan 1, 2001•10 citations

Ladder operators' normal ordering problem for quantum-deformed systems and the (q,p)-generalization of the Stirling and Bell numbers

A N F Aleixo, A. B. Balantekin

We resolve the ladder operators normal ordering problem for strings in the form for ( q , p )-deformed supersymmetric and shape-invariant potential systems, where n is a positive integer. We provide exact and explicit expressions for their normal form , where in all are at the right-hand side, and find that the solution involves expansion-coefficients sequence which corresponds to the generalization, for any ( q , p )-deformed shape-invariant potential system, of the classical Stirling and Bell numbers. We show that these numbers are given for expressions depending on parameters related to the forms of supersymmetric partner potentials and the system quantum deformation. We apply the general formalism to Pöschl–Teller, Morse and Scarf potential systems.

Journal of Physics A Mathematical and Theoretical•Jun 15, 2010•3 citations

An algebraic construction of generalized coherent states associated withq-deformed models for primary shape-invariant systems

A N F Aleixo, A. B. Balantekin

Generalized coherent states for primary shape invariant potential systems quantum deformed by different models are constructed using an algebraic approach based on supersymmetric quantum mechanics. We show that this generalized formalism is able (a) to supply the essential requirements necessary to establish a connection between classical and quantum formulations of a given system, (b) to reproduce, as particular cases, results already known for shape-invariant systems (such as standard harmonic oscillator and Pöschl–Teller potentials as well as quantum deformed harmonic oscillator models) and (c) point to a formalism that provides a unified description of the different kind of coherent states for quantum systems, deformed or not deformed.

Journal of Physics A Mathematical and Theoretical•Mar 14, 2007•11 citations

A Note on Deformed Ladder Operators for Noncommutative Morse Oscillator

A.H. Nadhira, Nurisya Mohd Shah, Chan, K. T.

Morse oscillator is one of the known solvable potentials which attracts many applications in quantum mechanics especially in quantum chemistry. One of the interesting results of this study is the generation of ladder operators for Morse potential. The operators are a representation of the shifting energy levels of the states exhibited by the wavefunction. From this result, we manipulate and deform the operators in such a way that it gives a noncommutative property to promote noncommutative quantum mechanics (NCQM). The resultant NC feature can be shown in the spatial coordinates and finally the Hamiltonian. In this study, we consider two-dimensional Morse potential where the ladder operators are in the form of the corresponding 2D Morse.

arXiv:1905.05183•May 13, 2019•0 citations
A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q -deformed ladder operators. We show that these new ladder operators satisfy new q -deformed commutation relations. In this context we construct an alternative q -deformed model that preserves the shape-invariance property presented by the primary system. q -deformed generalizations of Morse, Scarf and Coulomb potentials are given as examples.
The generalized purely squeezed states for primary shape-invariant potentials systems, quantum deformed by different models, are constructed by the ladder-operator method within an algebraic approach based on supersymmetric quantum mechanics. The characteristic properties of these states as well as their quantum statistical properties and squeezing effects for generalized quadrature observables are studied and analyzed in terms of the quantum deformation parameter q. An application is given for a quantum deformed Pöschl–Teller potential system, and numerical results are presented and discussed in detail.
We resolve the ladder operators normal ordering problem for strings in the form for ( q , p )-deformed supersymmetric and shape-invariant potential systems, where n is a positive integer. We provide exact and explicit expressions for their normal form , where in all are at the right-hand side, and find that the solution involves expansion-coefficients sequence which corresponds to the generalization, for any ( q , p )-deformed shape-invariant potential system, of the classical Stirling and Bell numbers. We show that these numbers are given for expressions depending on parameters related to the forms of supersymmetric partner potentials and the system quantum deformation. We apply the general formalism to Pöschl–Teller, Morse and Scarf potential systems.
Generalized coherent states for primary shape invariant potential systems quantum deformed by different models are constructed using an algebraic approach based on supersymmetric quantum mechanics. We show that this generalized formalism is able (a) to supply the essential requirements necessary to establish a connection between classical and quantum formulations of a given system, (b) to reproduce, as particular cases, results already known for shape-invariant systems (such as standard harmonic oscillator and Pöschl–Teller potentials as well as quantum deformed harmonic oscillator models) and (c) point to a formalism that provides a unified description of the different kind of coherent states for quantum systems, deformed or not deformed.
Morse oscillator is one of the known solvable potentials which attracts many applications in quantum mechanics especially in quantum chemistry. One of the interesting results of this study is the generation of ladder operators for Morse potential. The operators are a representation of the shifting energy levels of the states exhibited by the wavefunction. From this result, we manipulate and deform the operators in such a way that it gives a noncommutative property to promote noncommutative quantum mechanics (NCQM). The resultant NC feature can be shown in the spatial coordinates and finally the Hamiltonian. In this study, we consider two-dimensional Morse potential where the ladder operators are in the form of the corresponding 2D Morse.