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

College Physics

The method of Lie algebra in quantum transformation

MU Hai-feng

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

By means of the generators of Lie algebra,a unitary operator can be obtained.A concise diagonalization approach for coupled Boson quadratic Hamiltonation is also given.

Related papers

Diagonalization of the Rabi Hamiltonian by means of a unitary transformation

V. Denner, M. Wagner

The European Physical Journal B•Sep 1, 1985•3 citations

On the algebraic approach to the time-dependent quadratic Hamiltonian

Inés Urdaneta, Lourdes Sandoval, Alejandro Palma

The unitary operator V ( t ) that diagonalizes the time-dependent quadratic Hamiltonian (TDQH) into a time-dependent harmonic oscillator (TDHO) is obtained using a Lie algebra. The method involves a factorization of the TDQH into a TDHO through a unitary Bogoliubov transformation in terms of creation and annihilation operators with time-dependent coefficients. It is shown that this operator can be easily achieved by means of the factorization, together with the commonly known Wei–Norman theorem. We discuss the conditions under which this unitary operator converges to the evolution operator U ( t ) of the Schrödinger equation for the TDQH, giving then a straightforward calculation of the evolution operator with respect to the procedures published in the literature.

Journal of Physics A Mathematical and Theoretical•Aug 16, 2010•3 citations

Unitary representations of lie groups in quantum mechanics

Lochlainn O'Raifeartaigh

Springer eBooks•Apr 6, 2008•6 citations

An SU(1,1) Boson Realization Involved in Solving the Three Coupled Harmonic Oscillators' Problem

Hong-Yi Fan

We find that a three-mode boson realization of the SU(1,1) Lie algebra is involved in solving the three coupled harmonic oscillators' problem. The unitary operator U, which is found to be able to transform the Fock space of a three–dimensional isotropic harmonic oscillator into the space in which the Hamiltonian of three coupled oscillators is diagonized, is further decomposed as a quantum–mechanical rotation in three–mode Hilbert space followed by an SU(1,1) squeezing transformation. The coordinate representation of this SU(1,1) unitary operator is obtained.

Communications in Theoretical Physics•Sep 1, 1991•1 citation

Solving a Generalized Jaynes-Cummings Model by Supersymmetric Unitary Transformation

Lu Huai-Xin, Wang Xiao-Qin, Fan Hong-Yi

For the generalized Jaynes-Cummings model Hamiltonian which can describe two collectively radiation atoms, we find its supersymmetric structure. Based on supersymmetric quantum mechanics theory, we introduce a supersymmetric unitary transformation, in which the supersymmetric unitary transformation operator can be constructed by supersymmetric generators of the super-Lie algebra, to diagonalize the Hamiltonian. On doing so, its eigenvalue and eigenstates are obtained.

Chinese Physics Letters•May 1, 2000•8 citations

Lie algebra and unitarily invariant decomposition of Hermitian operators

Chia‐Chung Sun, Xue‐Qui Li, Auchin Tang

Abstract The unitarily invariant decomposition of Hermitian operators is performed by means of Lie algebra.

International Journal of Quantum Chemistry•Apr 1, 1984•15 citations
The unitary operator V ( t ) that diagonalizes the time-dependent quadratic Hamiltonian (TDQH) into a time-dependent harmonic oscillator (TDHO) is obtained using a Lie algebra. The method involves a factorization of the TDQH into a TDHO through a unitary Bogoliubov transformation in terms of creation and annihilation operators with time-dependent coefficients. It is shown that this operator can be easily achieved by means of the factorization, together with the commonly known Wei–Norman theorem. We discuss the conditions under which this unitary operator converges to the evolution operator U ( t ) of the Schrödinger equation for the TDQH, giving then a straightforward calculation of the evolution operator with respect to the procedures published in the literature.
We find that a three-mode boson realization of the SU(1,1) Lie algebra is involved in solving the three coupled harmonic oscillators' problem. The unitary operator U, which is found to be able to transform the Fock space of a three–dimensional isotropic harmonic oscillator into the space in which the Hamiltonian of three coupled oscillators is diagonized, is further decomposed as a quantum–mechanical rotation in three–mode Hilbert space followed by an SU(1,1) squeezing transformation. The coordinate representation of this SU(1,1) unitary operator is obtained.