Journal of Physics A Mathematical and General

Transition amplitudes for time-dependent linear harmonic oscillators

M. A. Rashid, Abubakar Mahmood

Published Sep 21, 2001• 1 citation

Abstract

Following standard operator techniques, we obtain the transition amplitudes for a general time-dependent linear harmonic oscillator without using the Green function, the calculation of which is quite difficult. Our method provides a straightforward and manifest method for calculating these transition amplitudes.

DOI: 10.1088/0305-4470/34/39/316

Related papers

Transition amplitudes for time-dependent harmonic oscillators

Leon F. Landovitz, Alfred M. Levine, W. M. Schreiber

Utilizing the Green’s function for a time dependent harmonic oscillator, we calculate the corresponding transition amplitudes. Particular examples of damped and runaway oscillators are discussed.

Journal of Mathematical PhysicsAug 1, 198027 citations

Time dependent linear quantum systems

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

The solution to the linear Heisenberg equations which result from the most general quadratic time dependent Hamiltonian is developed. The Green’s function is obtained, and the transition amplitudes between harmonic states are calculated.

The Journal of Chemical PhysicsJan 1, 198316 citations

An alternative derivation of transition amplitudes for time-dependent harmonic oscillators

H. E. De Meyer, Guido Vanden Berghe

It is shown that the relations which link the x and p operators of a time-dependent harmonic oscillator to the x and p operators of the corresponding time-independent oscillator can be cast into a generalized Bogoliubov transformation on the standard harmonic oscillator boson creation and annihilation operators. Once this fact has been recognized, various techniques can be invoked to derive in a short way transition amplitudes.

Journal of Mathematical PhysicsJul 1, 19813 citations

Transition probabilities for the driven harmonic oscillator

Francisco Marcelo Fernández

A simple and straightforward method is presented for calculating transition probabilities for the driven harmonic oscillator. The procedure does not require the explicit calculation of neither the time-evolution operator nor the Green’s function. As a result, a recurrence relation for the transition probabilities is obtained.

The Journal of Chemical PhysicsNov 15, 19874 citations

Time-dependent harmonic oscillators in an electromagnetic field

S -W Qian, Yayun Hu, J -S Wang

The authors consider the most general form of time-dependent charged harmonic oscillators in an electromagnetic field. The quantum mechanical solution is developed and the Green function is derived. Furthermore, they use gauge-invariant formulation of quantum mechanics to obtain the transition probabilities in the electric dipole approximation.

Journal of Physics A Mathematical and GeneralJul 11, 19871 citation

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 PhysicsJan 1, 20020 citations