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

The Journal of Chemical Physics

Wave-Interference Effects for a Forced Harmonic Oscillator

Wilbert James Lick

Published Oct 1, 1967• 0 citations
Publisher

Abstract

Wave-interference effects for transitions between unperturbed states of a forced harmonic oscillator are explicitly demonstrated by comparing the exact quantum-mechanical solution for this problem with a solution which assumes transitions to the different states are independent and therefore neglects wave-interference effects.
DOI
10.1063/1.1703327

Related papers

Note on the time-dependent damped and forced harmonic oscillator

P. G. L. Leach

A Hamiltonian for the time-dependent damped and forced harmonic oscillator is derived. A simple time-dependent linear canonical transformation transforms the Hamiltonian to one whose solution is readily obtained. The wave function for the corresponding quantum mechanical problem is given.

American Journal of Physics•Dec 1, 1978•16 citations

The quantum mechanical linearly damped forced oscillator

Leon F. Landovitz, Alfred M. Levine, E. Ozizmir +1 more

The solution is obtained to the quantum mechanical linearly damped harmonic oscillator subjected to a time dependent driving force. This solution allows the calculation of interesting quantum quantities such as the Green’s function and the transition amplitudes between harmonic oscillator states. The specific results for a harmonic driving force are given.

The Journal of Chemical Physics•May 15, 1983•7 citations

A concise quantum mechanical treatment of the forced damped harmonic oscillator

Ti Li

Abstract By selecting a right generalized coordinate X, which contains the general solutions of the classical motion equation of a forced damped harmonic oscillator, we obtain a simple Hamiltonian which does not contain time for the oscillator such that Schrödinger equation and its solutions can be directly written out in X representation. The wave functin in x representation are also given with the help of the eigenfunctions of the operator $$ \hat X $$ in x representation. The evolution of $$ \left\langle {\hat x} \right\rangle $$ is the same as in the classical mechanics, and the uncertainty in position is independent of an external influence; one part of energy mean is quantized and attenuated, and the other is equal to the classical energy.

Open Physics•Jul 31, 2008•0 citations

The forced harmonic oscillator: Coherent states and the RWA

Luis Octavio Castaños-Cervantes, Arturo Zúñiga-Segundo

We consider a forced harmonic oscillator in one-dimension. Using coherent states, we show that the treatment of the system is simplified, that the relationship between the classical and quantum solutions becomes transparent, and that the evolution operator of the system can be calculated easily as the free evolution operator of the harmonic oscillator followed by a displacement operator that depends on the classical solution. In addition, we consider the system in the rotating-wave-approximation (RWA), an application of the Averaging Theorem. We determine the relationship between the exact solution and the one in the RWA, test the accuracy of the RWA, and explain why the RWA gives accurate results in the realm of cavity quantum electrodynamics. Finally, we apply the results to a charged particle interacting with an electromagnetic field.

American Journal of Physics•Sep 18, 2019•15 citations

The exact solution of the transition probability of a harmonic oscillator under time-dependent external uniform field

Bing Yuan

The exact wave functions of a time-dependent driven harmonic oscillator are obtained by the trial function method and the exact transition probability are calculated.

College Physics•Jan 1, 2002•0 citations

Miscellanea in Elementary Quantum Mechanics, II

K. Husimi

It is a rather curious fact that the exact quantal treatment of forced oscillation has only recently been discovered to be feasible. There may be a lot of general arguments which make the possibility of such a treatment very convincing, but I myself find the ground for it in an elementary observation that the wave equation of forced harmonic oscillation, including the case of subharmonic resonance, admits a solution of Gaussian type, i.e. of the form: an exponential of a quadratic. On this basis the complete solution and the related problems are analyzed here.

Progress of Theoretical Physics•Apr 1, 1953•482 citations
Abstract By selecting a right generalized coordinate X, which contains the general solutions of the classical motion equation of a forced damped harmonic oscillator, we obtain a simple Hamiltonian which does not contain time for the oscillator such that Schrödinger equation and its solutions can be directly written out in X representation. The wave functin in x representation are also given with the help of the eigenfunctions of the operator X^ \hat X X^ in x representation. The evolution of ⟨x^⟩ \left\langle {\hat x} \right\rangle ⟨x^⟩ is the same as in the classical mechanics, and the uncertainty in position is independent of an external influence; one part of energy mean is quantized and attenuated, and the other is equal to the classical energy.
We consider a forced harmonic oscillator in one-dimension. Using coherent states, we show that the treatment of the system is simplified, that the relationship between the classical and quantum solutions becomes transparent, and that the evolution operator of the system can be calculated easily as the free evolution operator of the harmonic oscillator followed by a displacement operator that depends on the classical solution. In addition, we consider the system in the rotating-wave-approximation (RWA), an application of the Averaging Theorem. We determine the relationship between the exact solution and the one in the RWA, test the accuracy of the RWA, and explain why the RWA gives accurate results in the realm of cavity quantum electrodynamics. Finally, we apply the results to a charged particle interacting with an electromagnetic field.
It is a rather curious fact that the exact quantal treatment of forced oscillation has only recently been discovered to be feasible. There may be a lot of general arguments which make the possibility of such a treatment very convincing, but I myself find the ground for it in an elementary observation that the wave equation of forced harmonic oscillation, including the case of subharmonic resonance, admits a solution of Gaussian type, i.e. of the form: an exponential of a quadratic. On this basis the complete solution and the related problems are analyzed here.