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

Revista Mexicana de Física

The initial value problem method for time-dependent harmonic oscillator

Surarit Pepore

Published Jan 1, 2017• 1 citation
Publisher

Abstract

The initial value problem method is formulated to calculate the propagator for time- dependent harmonic oscillators. The method is based on finding the initial position operator from Heisenberg equations. The investigated models in this paper are the damped harmonic oscillator, the harmonic oscillator with strongly pulsating mass, and the harmonic oscillator with mass growing with time. The comparison of the initial value problem method with Feynman path integral and Schwinger method is also described.

DOI
10.31349/revmexfis.63.5.461

Related papers

The propagators for time-dependent mass harmonic oscillators

Surarit Pepore

In this paper, the propagator for a harmonic oscillator with mass obeying the function of m(t)=mtan2νt is derived by the Feynman path integral method. The wave function of this oscillator is calculated by expanding the obtained propagator. The propagator for a harmonic oscillator with strongly pulsating mass is evaluated by the Schwinger method. The propagator for a harmonic oscillator with mass rapidly growing with time is calculated by applying the integrals of the motion of quantum systems. The comparison between these methods are also discussed.

Physics & Astronomy International Journal•Nov 23, 2021•0 citations

Schwinger Method and Feynman Path Integral for a Harmonic Oscillator with Mass Growing with Time

Surarit Pepore, Bodinchat Sukbot

The exact propagator for a harmonic oscillator with mass growing like m(1+ατ )2 where m and α are constants and τ is time, is derived by the Schwinger method and the Feynman path integral. In the Schwinger formalism, the propagator can be calculated by basic operator algebra and elementary integrations. In the Feynman path integral method, it can be shown that such a propagator can be evaluated from that for a classical action with the application of a Pauli-Van Vleck formula.

Chinese Journal of Physics•Jun 1, 2015•4 citations

Path Integral for a Harmonic Oscillator with Time-Dependent Mass and Frequency

Surarit Pepore, P. Winotai, Tanakorn Osotchan +1 more

The exact solutions to the time-dependent Schrodinger equation for a harmonic oscillator with time-dependent mass and frequency were derived in a general form. The quantum mechanical propagator was calculated by the Feynman path integral method, while the wave function was derived from the spectral representation of the obtained propagator. It was shown that the propagator and the wave function depended on the s solution of a classical oscillator, in which the amplitude and phase satisfied the auxiliary equations. To demonstrate the derivation of the solution from our auxiliary equations, exponential and periodic functions of mass with constant frequency were imposed to evaluate the propagator and wave function for the Caldirola-Kanai and pulsating mass oscillators, respectively.

•Jan 1, 2006•6 citations

Integrals of the motion and green functions for time-dependent mass harmonic oscillators

Surarit Pepore

The application of the integrals of the motion of a quantum system in deriving Green function or propagator is established. The Greenfunction is shown to be the eigenfunction of the integrals of the motion which described initial points of the system trajectory in the phasespace. The explicit expressions for the Green functions of the damped harmonic oscillator, the harmonic oscillator with strongly pulsatingmass, and the harmonic oscillator with mass growing with time are obtained in co-ordinate representations. The connection between theintegrals of the motion method and other method such as Feynman path integral and Schwinger method are also discussed.

Revista Mexicana de Física•Jan 30, 2018•6 citations

Propagators for a particle in a time-dependent linear potential and a free particle

Surarit Pepore, R Biswas

In this paper, the propagators for a particle moving in a time-dependent linear potential and a free particle with linear damping are calculated by the application of the integrals of the motion of a quantum system. The propagator for a charged harmonic oscillator is derived from the Feynman path integrals and the propagator for a damped harmonic oscillator is evaluated by the Schwinger method. The relation between the integrals of the motion, Feynman path integrals, and Schwinger method are also described.

Physics & Astronomy International Journal•Oct 19, 2021•1 citation

Path integral for new models of time-dependent harmonic oscillators

Badri Berrabah, Baya Bentag

We have presented a particular direct method to solve time-dependent quantum problems within the framework of path integrals by using explicitly time-dependent transformations. We have applied it to the case of harmonic oscillator with time-dependent mass and frequency. Some examples have illustrated the method used. From their exact propagators, normalized solutions have been obtained.

International Journal of Geometric Methods in Modern Physics•Dec 12, 2019•1 citation
The initial value problem method is formulated to calculate the propagator for time- dependent harmonic oscillators. The method is based on finding the initial position operator from Heisenberg equations. The investigated models in this paper are the damped harmonic oscillator, the harmonic oscillator with strongly pulsating mass, and the harmonic oscillator with mass growing with time. The comparison of the initial value problem method with Feynman path integral and Schwinger method is also described.
In this paper, the propagator for a harmonic oscillator with mass obeying the function of m(t)=mtan2νt is derived by the Feynman path integral method. The wave function of this oscillator is calculated by expanding the obtained propagator. The propagator for a harmonic oscillator with strongly pulsating mass is evaluated by the Schwinger method. The propagator for a harmonic oscillator with mass rapidly growing with time is calculated by applying the integrals of the motion of quantum systems. The comparison between these methods are also discussed.
The exact solutions to the time-dependent Schrodinger equation for a harmonic oscillator with time-dependent mass and frequency were derived in a general form. The quantum mechanical propagator was calculated by the Feynman path integral method, while the wave function was derived from the spectral representation of the obtained propagator. It was shown that the propagator and the wave function depended on the s solution of a classical oscillator, in which the amplitude and phase satisfied the auxiliary equations. To demonstrate the derivation of the solution from our auxiliary equations, exponential and periodic functions of mass with constant frequency were imposed to evaluate the propagator and wave function for the Caldirola-Kanai and pulsating mass oscillators, respectively.
The application of the integrals of the motion of a quantum system in deriving Green function or propagator is established. The Greenfunction is shown to be the eigenfunction of the integrals of the motion which described initial points of the system trajectory in the phasespace. The explicit expressions for the Green functions of the damped harmonic oscillator, the harmonic oscillator with strongly pulsatingmass, and the harmonic oscillator with mass growing with time are obtained in co-ordinate representations. The connection between theintegrals of the motion method and other method such as Feynman path integral and Schwinger method are also discussed.
In this paper, the propagators for a particle moving in a time-dependent linear potential and a free particle with linear damping are calculated by the application of the integrals of the motion of a quantum system. The propagator for a charged harmonic oscillator is derived from the Feynman path integrals and the propagator for a damped harmonic oscillator is evaluated by the Schwinger method. The relation between the integrals of the motion, Feynman path integrals, and Schwinger method are also described.