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:hep-th/9410186 · Journal of Physics A Mathematical and General

slq(2) realizations for Kepler and oscillator potentials and q-canonical transformations

Omer Faruk Dayi, I. H. Duru

Published Apr 21, 1995• 14 citations
arXivHTMLPDF

Abstract

The realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2,1) of the Kepler and oscillator potentials are q-deformed. The q-canonical transformation connecting two realizations is given and a general definition for the q-canonical transformation is deduced. A q-Schrodinger equation for a Kepler-like potential is obtained from the q-oscillator Schrodinger equation. The energy spectrum and the ground-state wavefunction are calculated.

DOI
10.1088/0305-4470/28/8/029

Related papers

q-Schrödinger Equations for V = u2 + 1/u2 and Morse Potentials in Terms of the q-Canonical Transformation

Omer Faruk Dayi, I. H. Duru

The realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2,1) of the Schrödinger equations for the Morse and the V = u2 + 1/u2 potentials were known to be related by a canonical transformation. q-deformed analog of this transformation connecting two different realizations of the sl q(2) algebra is presented. By the virtue of the q-canonical transformation, a q-deformed Schrödinger equation for the Morse potential is obtained from the q-deformed V = u2 + 1/u2 Schrödinger equation. Wave functions and eigenvalues of the q-Schrödinger equations yielding a new definition of the q-Laguerre polynomials are studied.

arXiv:hep-th/9510015•International Journal of Modern Physics A•May 20, 1997•11 citations

q-Deformed Schrödinger Equation

Mircea Micu

We found hermitian realizations of the position vector $\vec{r}$, angular momentum $\vecΛ$ and linear momentum $\vec{p}$ behaving like vectors with respect to the $SU_q(2)$ algebra, generated by $L_0$ and $L_\pm$. They are used to write the $q$ deformed Schrödinger equation, whose solution for Coulomb and oscillator potential are briefly discussed.

arXiv:q-alg/9703026•Mar 13, 1997•1 citation

Ansu(1, 1) algebraic approach for the relativistic Kepler–Coulomb problem

M. Salazar–Ramírez, Daniel Martínez, R. D. Mota +1 more

We apply the Schrödinger factorization method to the radial second-order equation for the relativistic Kepler-Coulomb problem. From these operators we construct two sets of one-variable radial operators which are realizations for the $su(1,1)$ Lie algebra. We use this algebraic structure to obtain the energy spectrum and the supersymmetric ground state for this system.

arXiv:1006.3233•Journal of Physics A Mathematical and Theoretical•Oct 11, 2010•11 citations

Aq-deformed Schrödinger equation

M Micu

We found Hermitian realizations of the position vector , the angular momentum and the linear momentum , all behaving like vectors under the su q (2) algebra, generated by L 0 and L ± . They are used to introduce a q -deformed Schrödinger equation. Its solutions for the particular cases of the Coulomb and the harmonic oscillator potentials are given and briefly discussed.

arXiv:math-ph/9904011•Journal of Physics A Mathematical and General•Oct 21, 1999•17 citations

A q-deformed oscillator system with quantum group SLq(l) symmetry

Chang-Pu Sun, Xu‐Feng Liu, Jing-fa Lu +1 more

A q-deformed oscillator system with quantum group SL q (l) symmetry is constructed in terms of the q-deformed boson operators. The energy level degeneracy associated with the irreducible representation of SL q (l) is analysed, especially for the case that q is a root of unity.

Journal of Physics A Mathematical and General•Jan 21, 1992•3 citations

Quadratic algebras and position-dependent mass Schrödinger equations

C. Quesne

During recent years, exact solutions of position-dependent mass Schrödinger equations have inspired intense research activities, based on the use of point canonical transformations, Lie algebraic methods or supersymmetric quantum mechanical techniques. Here we highlight the interest of another approach to such problems, relying on quadratic algebras. We illustrate this point by constructing spectrum generating algebras for a class of d -dimensional radial harmonic oscillators with d ≥ 2 (including the one-dimensional oscillator on the line via some minor changes) and a specific mass choice. This provides us with a counterpart of the well-known su(1, 1) Lie algebraic approach to the constant-mass oscillators.

arXiv:0712.1971•Journal of Physics Conference Series•Aug 1, 2008•2 citations
The realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2,1) of the Kepler and oscillator potentials are q-deformed. The q-canonical transformation connecting two realizations is given and a general definition for the q-canonical transformation is deduced. A q-Schrodinger equation for a Kepler-like potential is obtained from the q-oscillator Schrodinger equation. The energy spectrum and the ground-state wavefunction are calculated.
The realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2,1) of the Schrödinger equations for the Morse and the V = u2 + 1/u2 potentials were known to be related by a canonical transformation. q-deformed analog of this transformation connecting two different realizations of the sl q(2) algebra is presented. By the virtue of the q-canonical transformation, a q-deformed Schrödinger equation for the Morse potential is obtained from the q-deformed V = u2 + 1/u2 Schrödinger equation. Wave functions and eigenvalues of the q-Schrödinger equations yielding a new definition of the q-Laguerre polynomials are studied.
We found hermitian realizations of the position vector r⃗\vec{r}r, angular momentum Λ⃗\vecΛΛ and linear momentum p⃗\vec{p}p​ behaving like vectors with respect to the SUq(2)SU_q(2)SUq​(2) algebra, generated by L0L_0L0​ and L±L_\pmL±​. They are used to write the qqq deformed Schrödinger equation, whose solution for Coulomb and oscillator potential are briefly discussed.
We apply the Schrödinger factorization method to the radial second-order equation for the relativistic Kepler-Coulomb problem. From these operators we construct two sets of one-variable radial operators which are realizations for the su(1,1)su(1,1)su(1,1) Lie algebra. We use this algebraic structure to obtain the energy spectrum and the supersymmetric ground state for this system.
During recent years, exact solutions of position-dependent mass Schrödinger equations have inspired intense research activities, based on the use of point canonical transformations, Lie algebraic methods or supersymmetric quantum mechanical techniques. Here we highlight the interest of another approach to such problems, relying on quadratic algebras. We illustrate this point by constructing spectrum generating algebras for a class of d -dimensional radial harmonic oscillators with d ≥ 2 (including the one-dimensional oscillator on the line via some minor changes) and a specific mass choice. This provides us with a counterpart of the well-known su(1, 1) Lie algebraic approach to the constant-mass oscillators.