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

Journal of Xi'an University of Post and Telecommunications

Solving one-dimensional harmonic oscillator with general form by sympletic transformation

Xiao-Qiang Xi

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

One-dimensional harmonic oscillator with general form is diagonalized as standard form by sympletic transformation.Then,we obtain energy level and wave function of it with occupation number representation.

Related papers

Several Solutions to Solving One-Dimensional Harmonic Oscillator's Energy Level

Xuehua Jiang

One-dimensional harmonic oscillator's energy eigenvalue is solved by the ways of energy way,raising-and-lowering operator way,coherent state way and double wave function way.Several simple ways of solving harmonic oscillator's energy level are given.

Journal of Yueyang Normal University•Jan 1, 2002•0 citations

Several Solutions to Solving Harmonic Oscillator's Energy Eigenvalue

Jiang Xue

One dimensional harmonic oscillator's energy eigenvalue is solved by the ways o f matrix dynamics way,raising and lowering operator way,coherent state way and double wave function way.Several simple ways of solving harmonic oscillator's en ergy level are given.

Journal of Nanyang Normal University•Jan 1, 2002•0 citations

Solving energy eigenvalue of n module coupling harmonic oscillators by virtue of quadratic form

Yunhai Zhang

A unitary matrix is constructed by virtue of quadratic form theory for coordinates and momentums transformation.The Hamiltonian of the n-D coupling harmonic oscillators is diagonalized by means of the transformation.The exact solution of energy spectrum of n-D coupling quantum harmonic oscillator is given.It also offers a general mathematic method solving problems of this kind.

College Physics•Jan 1, 2009•0 citations

Quantum Harmonic Oscillators in One and Two Dimensions

Guanghan Xia

The Schrödinger equation is a significant achievement on the development of quantum mechanics. By solving the Schrödinger equation, the fundamental behaviors and properties of a microscopic particle can be found in one- to three-dimensions. The article focuses on the derivations of quantum harmonic oscillators in one dimension by solving second order-differential equation. The wave functions, probability densities under different energy levels are presented. The results can be used to estimate different forms of continuous potential experienced by an oscillator. By calculating the uncertainty relation of the oscillator under one specific excited state, the general relation can be confirmed. Based on the output, by splitting the variables, the two-dimensional harmonic oscillator can also be derived. The degenerate energy levels are presented as . Numerical simulations are made to visualize those results and suggests the relation of energy levels and number of maxima of the probability densities.

Highlights in Science Engineering and Technology•Aug 21, 2023•0 citations

Study on Perturbed Harmonic Oscillator by Particle-Number Representation

Xie Quan

Perturbed harmonic oscillator's approximate values of energy level and wave function could be easily calculated by particle-number representation.The proccess is very complicated if it is calculated by coordinate representation.The applicability to solve perturbation of harmonic oscillator by particle-number representation is ascertained due to the study on a example.

Journal of Xinyang Normal University•Jan 1, 2010•0 citations

An algebraic approach to the generalization of n-dimensional coupled harmonic oscillators system

Jin Ming-Jie, Lei Tan

Using the quadratic form theory, we achieve the decoupling of systematic Hamiltonian of generalization of n-dimensional coupled harmonic oscillators and derive the diagonalized Hamiltonian by three linear transformations with keeping the commutation relations unchanged. The energy eigenvalue and the eigenfunction of the system are also obtained.

Acta Physica Sinica•Jan 1, 2012•0 citations
The Schrödinger equation is a significant achievement on the development of quantum mechanics. By solving the Schrödinger equation, the fundamental behaviors and properties of a microscopic particle can be found in one- to three-dimensions. The article focuses on the derivations of quantum harmonic oscillators in one dimension by solving second order-differential equation. The wave functions, probability densities under different energy levels are presented. The results can be used to estimate different forms of continuous potential experienced by an oscillator. By calculating the uncertainty relation of the oscillator under one specific excited state, the general relation can be confirmed. Based on the output, by splitting the variables, the two-dimensional harmonic oscillator can also be derived. The degenerate energy levels are presented as . Numerical simulations are made to visualize those results and suggests the relation of energy levels and number of maxima of the probability densities.