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

Xiaogan Xueyuan xuebao

The Exact Results of Onedimensional Harmonic Oscillator Perturbated with Weak Electric Field within △t Time

Wu Xin

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

By using the method of Heisenberg picture,this paper makes an analytical research on the probability of onedimensional harmonic oscillator perturbated with weak electric field within △t time in all its states,and obtains the exact results.

Related papers

Calculation of the energy level of one-dimensional linear harmonic oscillator in weak electric field

Xie Yu-peng

Linear harmonic oscillator takes an important role in quantum mechanics.Many systems can be taken approximately as of linear harmonic oscillator.Consequently,the study on linear harmonic oscillator is significant in many ways.Using methods of formula and perturbation,this paper finds out the energy eigenvalue of one-dimensional linear harmonic oscillator in weak electric field,and presents clearly two typical solutions for the energy level of one-dimensional linear harmonic oscillator in weak electric field.

Journal of Jilin Institute of Chemical Technology•Jan 1, 2010•0 citations

Solution of Harmonic Oscillator Perturbed by Electric Field

Habtamu Dagnaw

The aim of this work is to analyze the energy eigen value of harmonic oscillator perturbed by electric field. In order to carry out the analysis, we have used two independent methods, suchas the perturbation method and time independent schrodinger equation. We have calculated the first order energy correction, second order energy correction , and the energy eigen value for time independent schrodinger equation. It has been found that the energy eigen value of harmonic oscillator is the same in two independent methods. Keywords: Harmonic ocillator, Electric Field, Perturbation Method , Eigen value. DOI : 10.7176/APTA/78-01 Publication date :June 30 th 2019

Advances in physics theories and applications•Jun 1, 2019•1 citation

Time-Dependent Perturbation Theory in Quantum Phase Space

Qian‐Shu Li

Time-dependent perturbation theory is discussed within the quantum phase space representation as formulated by Torres-Vega and Frederick(T-F) and the quantum transition probability is studied.Time-dependent perturbation formula in T-F quantum phase space is established,in accordance with the calculation theory in T-F phase space.As an example,the one dimensional harmonic oscillator system,affected by an external electric field,is used to calculate in T-F phase space,the result indicate that the principle of the method is correct.Quantum transition probability of the system's first excited state in T-F phase space is discussed.

Transactions of Beijing Institute of Technology•Jan 1, 2009•0 citations

Exact Solution of a Time-Dependent Quantal Harmonic Oscillator with a Singular Perturbation

Paolo Camiz, Anna Gerardi, Carlo Marchioro +2 more

The quantal problem of a particle interacting in one dimension with an external time-dependent quadratic potential and a constant inverse square potential is exactly solved. The solutions are found both in the Schrödinger representation, by using a generating function or a time-dependent raising operator, and in the Heisenberg picture. They depend only on the solution of the classical harmonic oscillator. The generalizations to the n-dimensional problem and to the problem of N particles in one dimension, interacting pairwise via a quadratic time-dependent potential and a constant inverse square potential, are finally sketched.

Journal of Mathematical Physics•Oct 1, 1971•84 citations

Algebraicalsolution to the energy level and wave function of one-dimensional harmonic oscillator

W. J. Chang

In the research of one-dimensional harmonic oscillaton as the object in Heisenberg’s picture. We have got two kinds of solutions of its energy level and wave fanction by algebraic approach of using matrix mechanics and factorization method.

Journal of Yunnan Normal University•Jan 1, 2001•0 citations

Heisenberg-picture approach to the exact quantum motion of a time-dependent forced harmonic oscillator

Hyeong-Chan Kim, Minho Lee, Jeong‐Young Ji +1 more

In the Heisenberg picture, the generalized invariant and exact quantum motions are found for a time dependent forced harmonic oscillator. We find the eigenstate and the coherent state of the invariant and show that the dispersions of these quantum states do not depend on the external force. Our formalism is applied to two interesting cases. \textcopyright{} 1996 The American Physical Society.

arXiv:quant-ph/9605046•Physical Review A•Jun 1, 1996•44 citations
Linear harmonic oscillator takes an important role in quantum mechanics.Many systems can be taken approximately as of linear harmonic oscillator.Consequently,the study on linear harmonic oscillator is significant in many ways.Using methods of formula and perturbation,this paper finds out the energy eigenvalue of one-dimensional linear harmonic oscillator in weak electric field,and presents clearly two typical solutions for the energy level of one-dimensional linear harmonic oscillator in weak electric field.
The aim of this work is to analyze the energy eigen value of harmonic oscillator perturbed by electric field. In order to carry out the analysis, we have used two independent methods, suchas the perturbation method and time independent schrodinger equation. We have calculated the first order energy correction, second order energy correction , and the energy eigen value for time independent schrodinger equation. It has been found that the energy eigen value of harmonic oscillator is the same in two independent methods. Keywords: Harmonic ocillator, Electric Field, Perturbation Method , Eigen value. DOI : 10.7176/APTA/78-01 Publication date :June 30 th 2019
Time-dependent perturbation theory is discussed within the quantum phase space representation as formulated by Torres-Vega and Frederick(T-F) and the quantum transition probability is studied.Time-dependent perturbation formula in T-F quantum phase space is established,in accordance with the calculation theory in T-F phase space.As an example,the one dimensional harmonic oscillator system,affected by an external electric field,is used to calculate in T-F phase space,the result indicate that the principle of the method is correct.Quantum transition probability of the system's first excited state in T-F phase space is discussed.
The quantal problem of a particle interacting in one dimension with an external time-dependent quadratic potential and a constant inverse square potential is exactly solved. The solutions are found both in the Schrödinger representation, by using a generating function or a time-dependent raising operator, and in the Heisenberg picture. They depend only on the solution of the classical harmonic oscillator. The generalizations to the n-dimensional problem and to the problem of N particles in one dimension, interacting pairwise via a quadratic time-dependent potential and a constant inverse square potential, are finally sketched.