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

Canadian Journal of Physics

Parametric-time coherent states for Morse potential

Nuri Ünal

Published Aug 1, 2002• 12 citations
Publisher

Abstract

We transform the Lagrangian of the Morse-potential problem into two harmonic oscillators in a new parametric time and quantize this system by using path integrals over holomorphic coordinates of oscillators and derive coherent states. PACS Nos.: 31.15-p, 03.65Ca, 03.65Ge
DOI
10.1139/p02-040

Related papers

Coherent states for PT-/non-PT-symmetric and non-Hermitian Morse potentials via the path integral method

Nalan Kandırmaz, R. Sever

We discuss the coherent states for PT-/non-PT-symmetric and non-Hermitian generalized Morse potentials obtained by using path integral formalism over the holomorphic coordinates. We transform the action of generalized Morse potentials into two harmonic oscillators with a new parametric time to establish the parametric time coherent states. We calculate the energy eigenvalues and the corresponding wave functions in parabolic coordinates.

arXiv:1003.2264•Physica Scripta•Mar 1, 2010•19 citations

Parametric time-coherent states for the hydrogen atom

Nuri Ünal

We obtained coherent states for the hydrogen atom by transforming the problem into four oscillators in the parametric time at a classical level, and quantizing these oscillators by using path integration over their holomorphic coordinates. We showed that for the negative- (positive-) energy coherent states the mean values of the physical position of the electron satisfy the Keplerian ellipses (hyperbolas) and that their dispersions oscillate (increase) in parametric time.

Physical Review A•Apr 16, 2001•13 citations

Coherent states and a path integral for the Morse oscillator

Christopher C. Gerry

Coherent states for the Morse oscillator are constructed using generalized coherent states associated with the SO(2,1) noninvariance group for this potential. By using the path integral over these states, it is shown that the Morse oscillator may be viewed as a harmonic oscillator evolving in a fictitious time. To show that this picture is mathematically consistent, we compute the path integral for the Green's function and recover the bound-state spectrum.

Physical Review A•Apr 1, 1986•60 citations

Coherent states for Kratzer-type potentials

Nalan Kandırmaz

The coherent states for a particle in Kratzer type potentials are constructed by solving Feynman’s path integral. The action of the generalized Kratzer potential is transformed into two harmonic oscillators by Levi-Civita transformation to derive the parametric time coherent states. Green’s function, energy eigenvalues, and the corresponding wave functions for this potential are calculated. The evaluated results are reduced to the modified Kratzer potentials and Kratzer-Fues oscillators which are special cases of the generalized Kratzer potential.

Journal of Mathematical Physics•Jun 1, 2018•6 citations

Coherent states for the Morse oscillator

Sabre Kais, Raphael David Levine

The explicit coordinate representation of coherent states for the Morse oscillator is derived and discussed, in the limit that the potential well is deep. Without this limit, such states can only be written as a finite sum that does evolve coherently but in a dilated time.

Physical Review A•Mar 1, 1990•69 citations

Quasi-coherent states for harmonic oscillator with time-dependent parameters

Nuri Ünal

In this study, we discuss the harmonic oscillator with the time-dependent frequency, ω(t), and the mass, M(t), by generalizing the holomorphic coordinates for the harmonic oscillator. In general cases, we solve the Schrödinger equation by reducing it into the Riccati equation and discuss the uncertainties for the quasi-coherent states of the time-dependent harmonic oscillator. In special cases, we find the following results: First, for a time-dependent harmonic oscillator, if [ω(t)M(t)] is constant, then the coherent states will evolve as the coherent states. Second, for the driven harmonic oscillator, the coherent states will evolve as the coherent states with new eigenvalues. Third, we derive quasi-coherent states for the Caldirola–Kanai Hamiltonian and show that the product of uncertainties, ΔxΔp, is larger than minimum value; however, it is constant. We also discuss the classical equations of motion for the system.

Journal of Mathematical Physics•Jan 1, 2012•13 citations
The coherent states for a particle in Kratzer type potentials are constructed by solving Feynman’s path integral. The action of the generalized Kratzer potential is transformed into two harmonic oscillators by Levi-Civita transformation to derive the parametric time coherent states. Green’s function, energy eigenvalues, and the corresponding wave functions for this potential are calculated. The evaluated results are reduced to the modified Kratzer potentials and Kratzer-Fues oscillators which are special cases of the generalized Kratzer potential.
In this study, we discuss the harmonic oscillator with the time-dependent frequency, ω(t), and the mass, M(t), by generalizing the holomorphic coordinates for the harmonic oscillator. In general cases, we solve the Schrödinger equation by reducing it into the Riccati equation and discuss the uncertainties for the quasi-coherent states of the time-dependent harmonic oscillator. In special cases, we find the following results: First, for a time-dependent harmonic oscillator, if [ω(t)M(t)] is constant, then the coherent states will evolve as the coherent states. Second, for the driven harmonic oscillator, the coherent states will evolve as the coherent states with new eigenvalues. Third, we derive quasi-coherent states for the Caldirola–Kanai Hamiltonian and show that the product of uncertainties, ΔxΔp, is larger than minimum value; however, it is constant. We also discuss the classical equations of motion for the system.