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

Results in Physics

Analysis of quantum energy for Caldirola–Kanai Hamiltonian systems in coherent states

Jeong Ryeol Choi

Published Jan 1, 2013• 15 citations
Publisher

Abstract

Abstract Quantum energies for Caldirola–Kanai Hamiltonian systems with and without a singular perturbation are investigated in coherent states on the basis of invariant operator theory. Our results are compared with those of several different approaches from various angles. Further, the advantages of our method over that adopted in the previous researches are addressed in detail.

DOI
10.1016/j.rinp.2013.06.003

Related papers

COHERENT STATES OF NONCONSERVATIVE HARMONIC OSCILLATOR WITH A SINGULAR PERTURBATION

Jeong Ryeol Choi

We investigated the coherent states of nonconservative harmonic oscillator with a singular perturbation. The invariant operator represented in terms of lowering and raising operators. We confirmed that if the difference between two eigenvalues, α and β, of coherent states is much larger than unity, the states |α> and |β> are approximately orthogonal to each another. We calculated the expectation values of various quantities such as invariant operator, Hamiltonian and mechanical energy in coherent state. The mechanical energy of the system described by the Kanai–Caldirola Hamiltonian decreased exponentially depending on γ as time goes by in coherent state.

International Journal of Modern Physics B•May 10, 2003•1 citation

Trajectory-coherent states for the Caldirola - Kanai Hamiltonian

A. G. Karavaev

In this paper we construct the trajectory-coherent states for the Caldirola - Kanai Hamiltonian. We investigate the properties of this states.

arXiv:quant-ph/9709009•Sep 4, 1997•2 citations

Thermodynamics of squeezed states for the Kanai-Caldirola Hamiltonian

J. Aliaga, G. Crespo, Araceli N. Proto

Using the maximum-entropy approach, we analyze the appearance of coherent and squeezed states for the Kanai-Caldirola Hamiltonian, making it possible to extend the analysis easily to the so-called generalized harmonic oscillator and a sort of two-photon Hamiltonian, for both the zero and nonzero temperature cases. A connection between the possibility of obtaining squeezing and the relevant operators included in the density matrix is shown. Finally, a comparison with pertinent previous results in the literature is also presented.

Physical Review A•Oct 1, 1990•17 citations

Analytical Computation of the Caldirola-Kanai Oscillator Parameters by the Dynamic Invariant Method

Chadia Qotni, Az-Eddine L. Marrakchi, Salaheddine Sayouri +1 more

The method of the invariant dynamical linear operator is very simple and may be useful to solve the Schrodinger equation, in particular in the case of the problem of a harmonic oscillator with a time dependent mass and frequency. Indeed, we have successfully used this approach to the Caldirola-Kanai oscillator. In particular, we have obtained explicit expressions of the uncertainty product and the quantum correlation coefficient. The results obtained are in good agreement with those of the literature.

Applied mathematics and physics•Oct 18, 2019•0 citations

The quantum Lane-Emden-type Kanai-Caldirola oscillators

Vagner Henrique Loiola Bessa, I. Guedes

We obtain the exact wave functions of two Lane-Emden-type Kanai-Caldirola (LE-KC) oscillators by using the dynamical invariant method. To do so, we analytically solve the respective Milne-Pinney equation for each oscillator. We also calculate the uncertainty product, the transition probability and the quantum-mechanical energy expectation value for each oscillator. We compare the results with those of the well-known KC oscillator. The quantum-mechanical energy expectation value of the KC oscillator goes to zero faster than that of the LE-KC oscillators, indicating that the KC system is more damped than the LE-KC ones.

Journal of Mathematical Physics•Dec 1, 2012•6 citations

Coherent states for the damped harmonic oscillator

Kyu Hwang Yeon, Chung‐In Um, Thomas F. George

Using the Caldirola-Kanai Hamiltonian for the damped harmonic oscillator, exact coherent states are constructed. These new coherent states satisfy the properties which coherent states should generally have.

Physical Review A•Dec 1, 1987•81 citations
Abstract Quantum energies for Caldirola–Kanai Hamiltonian systems with and without a singular perturbation are investigated in coherent states on the basis of invariant operator theory. Our results are compared with those of several different approaches from various angles. Further, the advantages of our method over that adopted in the previous researches are addressed in detail.
We investigated the coherent states of nonconservative harmonic oscillator with a singular perturbation. The invariant operator represented in terms of lowering and raising operators. We confirmed that if the difference between two eigenvalues, α and β, of coherent states is much larger than unity, the states |α> and |β> are approximately orthogonal to each another. We calculated the expectation values of various quantities such as invariant operator, Hamiltonian and mechanical energy in coherent state. The mechanical energy of the system described by the Kanai–Caldirola Hamiltonian decreased exponentially depending on γ as time goes by in coherent state.
Using the maximum-entropy approach, we analyze the appearance of coherent and squeezed states for the Kanai-Caldirola Hamiltonian, making it possible to extend the analysis easily to the so-called generalized harmonic oscillator and a sort of two-photon Hamiltonian, for both the zero and nonzero temperature cases. A connection between the possibility of obtaining squeezing and the relevant operators included in the density matrix is shown. Finally, a comparison with pertinent previous results in the literature is also presented.
The method of the invariant dynamical linear operator is very simple and may be useful to solve the Schrodinger equation, in particular in the case of the problem of a harmonic oscillator with a time dependent mass and frequency. Indeed, we have successfully used this approach to the Caldirola-Kanai oscillator. In particular, we have obtained explicit expressions of the uncertainty product and the quantum correlation coefficient. The results obtained are in good agreement with those of the literature.
We obtain the exact wave functions of two Lane-Emden-type Kanai-Caldirola (LE-KC) oscillators by using the dynamical invariant method. To do so, we analytically solve the respective Milne-Pinney equation for each oscillator. We also calculate the uncertainty product, the transition probability and the quantum-mechanical energy expectation value for each oscillator. We compare the results with those of the well-known KC oscillator. The quantum-mechanical energy expectation value of the KC oscillator goes to zero faster than that of the LE-KC oscillators, indicating that the KC system is more damped than the LE-KC ones.