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

Zeitschrift für Physikalische Chemie

Algebraic Approach to the Morse Potential and its Coherent States

Shi‐Hai Dong

Published Jan 1, 2002• 8 citations
Publisher

Abstract

A realization of the ladder operators for the 1D Morse potential is presented. These operators satisfy the SU(2) group. The case of anisotropic 3D Morse potential is also discussed if it can be regarded as three 1D Morse potential. The average values of some observables in the coherent states are also calculated.
DOI
10.1524/zpch.2002.216.1.103

Related papers

The SU(2) realization for the Morse potential and its coherent states

Shishan Dong

A realization of the raising and lowering operators for the Morse potential is presented. We show that these operators satisfy the commutation relations for the SU(2) group. Closed analytical expressions are derived for the matrix elements of different functions such as 1/y and d/dy. The harmonic limit of the SU(2) operators is also studied. The transition probability between two eigenstates produced by a harmonic perturbation as a function of the operators [Formula: see text]±,0 is discussed. The average values of some observables in the coherent states |α > for the Morse potential are also calculated. PACS Nos.: 02.30+b, 03.65Fd, 42.50Ar, and 33.10Cs

Canadian Journal of Physics•Feb 1, 2002•50 citations

Algebraic approach to the Kratzer potential

Mohammad Reza Setare, Ebrahim Karimi

In this paper, the energy eigenvalues and the corresponding eigenfunctions are calculated for the Kratzer potential. Then we obtain the ladder operators for the one-dimensional (1D) and 3D Kratzer potential. Finally, we show that these operators satisfy the SU(2) commutation relation.

Physica Scripta•Dec 5, 2006•101 citations

An algebraic construction of the coherent states of the Morse potential based on SUSY QM

Balázs Molnár, M. G. Benedict

By introducing the shape invariant Lie algebra spanned by the SUSY ladder operators plus the unity operator, a new basis is presented for the quantum treatment of the one-dimensional Morse potential. In this discrete, complete orthonormal set, which we call the pseudo number states, the Morse Hamiltonian is tridiagonal. By using this basis we construct coherent states algebraically for the Morse potential, in a close analogy with the harmonic oscillator. We also show that there exists an unitary displacement operator creating these coherent states from the ground state. We show that our coherent states form a continuous and overcomplete set of states. They coincide with a class of states constructed earlier by Nieto and Simmons by using the coordinate representation. \pacs{3.65.Fd, 02.20.Sv, 42.50.-p}

arXiv:quant-ph/9812041•Dec 16, 1998•0 citations

Ladder operators in the Morse potential obtained from a related harmonic oscillator

R. Montemayor, Luis F. Urrutia

In this paper we explore a similarity transformation between the Morse oscillator and the two-dimensional harmonic oscillator. This transformation enables us to determine in a simple and straightforward way, all ladder operators for the Morse oscillator and their associated algebra, avoiding the use of the factorization method.

American Journal of Physics•Jul 1, 1983•16 citations

A realization of the dynamical group for the square-well potential and its coherent states

R. Lemus, Alejandro Frank

A realization of the ladder operators for the infinitely deep well potential is presented. Both the asymmetric and symmetric wells are discussed. It is shown that these operators satisfy the commutation relations for the SU (1, 1) group. Closed analytical expressions for the matrix elements of some relevant functions are obtained. Perelomov coherent states for this system are explicitly constructed. The behaviour of the dispersion relation and the time evolution for such states are examined.

Journal of Physics A Mathematical and General•Apr 14, 2003•7 citations

Algebraic construction of the coherent states of the Morse potential based on supersymmetric quantum mechanics

M. G. Benedict, Balázs Molnár

By introducing the shape-invariant Lie algebra spanned by the supersymmetric ladder operators plus the identity operator, we generate a discrete complete orthonormal basis for the quantum treatment of the one-dimensional Morse potential. In this basis, which we call the pseudo-number-states, the Morse Hamiltonian is tridiagonal. Then we construct algebraically the continuous overcomplete set of coherent states for the Morse potential in close analogy with the harmonic oscillator. These states coincide with a class of states constructed earlier by Nieto and Simmons [Phys. Rev. D 20, 1342 (1979)] by using the coordinate representation. We also give the unitary displacement operator creating these coherent states from the ground state.

Physical Review A•Sep 1, 1999•93 citations
A realization of the raising and lowering operators for the Morse potential is presented. We show that these operators satisfy the commutation relations for the SU(2) group. Closed analytical expressions are derived for the matrix elements of different functions such as 1/y and d/dy. The harmonic limit of the SU(2) operators is also studied. The transition probability between two eigenstates produced by a harmonic perturbation as a function of the operators [Formula: see text]±,0 is discussed. The average values of some observables in the coherent states |α > for the Morse potential are also calculated. PACS Nos.: 02.30+b, 03.65Fd, 42.50Ar, and 33.10Cs
By introducing the shape invariant Lie algebra spanned by the SUSY ladder operators plus the unity operator, a new basis is presented for the quantum treatment of the one-dimensional Morse potential. In this discrete, complete orthonormal set, which we call the pseudo number states, the Morse Hamiltonian is tridiagonal. By using this basis we construct coherent states algebraically for the Morse potential, in a close analogy with the harmonic oscillator. We also show that there exists an unitary displacement operator creating these coherent states from the ground state. We show that our coherent states form a continuous and overcomplete set of states. They coincide with a class of states constructed earlier by Nieto and Simmons by using the coordinate representation. \pacs{3.65.Fd, 02.20.Sv, 42.50.-p}
By introducing the shape-invariant Lie algebra spanned by the supersymmetric ladder operators plus the identity operator, we generate a discrete complete orthonormal basis for the quantum treatment of the one-dimensional Morse potential. In this basis, which we call the pseudo-number-states, the Morse Hamiltonian is tridiagonal. Then we construct algebraically the continuous overcomplete set of coherent states for the Morse potential in close analogy with the harmonic oscillator. These states coincide with a class of states constructed earlier by Nieto and Simmons [Phys. Rev. D 20, 1342 (1979)] by using the coordinate representation. We also give the unitary displacement operator creating these coherent states from the ground state.