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

Acta Physica Sinica

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

Jin Ming-Jie, Lei Tan

Published Jan 1, 2012• 0 citations
Publisher

Abstract

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.

DOI
10.7498/aps.61.140301

Related papers

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

A quadratic approach to n-dimensional harmonic oscillator energy eigenvalue of coordinate and momentum coupling

Yi Jin

By means of quadratic theory,we present a general method to solve the energy eigenvalue of coordinate and momentum coupling of n-dimensional harmonic oscillator.To apply this method to solve the energy eigenvalue of two-dimensional and three-dimensional coupling harmonic oscillator,our conclusion is the same with the others.Since the present method does not require a specific form of transformation matrix,this makes it be simple to solve the eigenvalue of a symmetrical form Hamilton and easy to calculate the results.This method is a universal and very effective algebraic method.

College Physics•Jan 1, 2011•0 citations

Eigenvalues and Eigenfunction of N Modes Coupled Harmonic Oscillators

Long Zheng-Wen

Through coordinate transformation,Hamiltonian of N modes coupled harmonic oscillators could be expressed as the standard quadric form in new bases to eliminate the coupled items.As a result of calculation,a fact could be found that the new bases satisfy quasi-canonical commutation relation.By introducing quasi-particle’s creation and annihilation operators,the Hamiltonian could be simplified as N modes independent harmonic oscillators.Furthermore,the corresponding eigenvalues and eigenfunction could be obtained.

Journal of Wenzhou University•Jan 1, 2011•0 citations

Decoupling of the Heisenberg equations of motion and the diagonalization of the Hamiltonian

LI Feng-min

It is one of the important problems to solve the Schrodinger equation for the coupled harmonic oscillators.Here the Heisenberg equations of motion for the coupled harmonic oscillators are written in the form of Schrodinger type equation,which can be decoupled by certain transformation.Further,the Hamiltonian can be diagonalized.For the anisotropic harmonic oscillator in a background magnetic field,the diagonalization form of the Hamiltonian,the energy eigenvalues and the eigenstates are derived.Such a process of derivation has clear physical picture and is easy to understand.

Journal of Tianjin University of Technology and Education•Jan 1, 2012•0 citations

Coupled harmonic oscillator systems: An elementary algebraic decoupling approach

Tova Feldmann, M. Cohen, B. L. Burrows

We present simple explicit coordinate transformations which serve to decouple the Schrödinger equation for a pair of (not necessarily identical) harmonic oscillators in the presence of bilinear perturbing potentials. We derive general conditions for the decoupling, and give some examples of physical interest. These include the much studied example with just a static perturbation, the parallel problem with a dynamic coupling term, and the classic example of an isotropic two-dimensional oscillator in a transverse magnetic field, first solved by Fock (1928) by separation of variables.

Journal of Mathematical Physics•Sep 1, 2000•4 citations

On the quantum dynamics of a general time-dependent coupled oscillator

Rahma Zerimeche, Naima Mana, Maroua Sekhri +2 more

By using the Lewis–Riesenfeld invariants theory, we investigate the quantum dynamics of a two-dimensional (2D) time-dependent coupled oscillator. We introduce a unitary transformation and show the conditions under which the invariant operator is uncoupled to describe two simple harmonic oscillators with time-independent frequencies and unit masses. The decouplement allows us to easily obtain the corresponding eigenstates. The generalization to three-dimensional (3D) time-dependent coupled oscillator is briefly discussed where a diagonalized invariant, which is exactly the sum of three simple harmonic oscillators, is obtained under specific conditions on the parameters.

Modern Physics Letters B•Feb 20, 2023•1 citation
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.
By means of quadratic theory,we present a general method to solve the energy eigenvalue of coordinate and momentum coupling of n-dimensional harmonic oscillator.To apply this method to solve the energy eigenvalue of two-dimensional and three-dimensional coupling harmonic oscillator,our conclusion is the same with the others.Since the present method does not require a specific form of transformation matrix,this makes it be simple to solve the eigenvalue of a symmetrical form Hamilton and easy to calculate the results.This method is a universal and very effective algebraic method.
Through coordinate transformation,Hamiltonian of N modes coupled harmonic oscillators could be expressed as the standard quadric form in new bases to eliminate the coupled items.As a result of calculation,a fact could be found that the new bases satisfy quasi-canonical commutation relation.By introducing quasi-particle’s creation and annihilation operators,the Hamiltonian could be simplified as N modes independent harmonic oscillators.Furthermore,the corresponding eigenvalues and eigenfunction could be obtained.
It is one of the important problems to solve the Schrodinger equation for the coupled harmonic oscillators.Here the Heisenberg equations of motion for the coupled harmonic oscillators are written in the form of Schrodinger type equation,which can be decoupled by certain transformation.Further,the Hamiltonian can be diagonalized.For the anisotropic harmonic oscillator in a background magnetic field,the diagonalization form of the Hamiltonian,the energy eigenvalues and the eigenstates are derived.Such a process of derivation has clear physical picture and is easy to understand.
We present simple explicit coordinate transformations which serve to decouple the Schrödinger equation for a pair of (not necessarily identical) harmonic oscillators in the presence of bilinear perturbing potentials. We derive general conditions for the decoupling, and give some examples of physical interest. These include the much studied example with just a static perturbation, the parallel problem with a dynamic coupling term, and the classic example of an isotropic two-dimensional oscillator in a transverse magnetic field, first solved by Fock (1928) by separation of variables.
By using the Lewis–Riesenfeld invariants theory, we investigate the quantum dynamics of a two-dimensional (2D) time-dependent coupled oscillator. We introduce a unitary transformation and show the conditions under which the invariant operator is uncoupled to describe two simple harmonic oscillators with time-independent frequencies and unit masses. The decouplement allows us to easily obtain the corresponding eigenstates. The generalization to three-dimensional (3D) time-dependent coupled oscillator is briefly discussed where a diagonalized invariant, which is exactly the sum of three simple harmonic oscillators, is obtained under specific conditions on the parameters.