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

Reports on Mathematical Physics

General solutions of quantum mechanical equations of motion with time-dependent hamiltonians: A lie algebraic approach

Maciej Kuna, Jan Naudts

Published Jan 1, 2010• 22 citations
Publisher
DOI
10.1016/s0034-4877(10)80007-2

Related papers

Lie algebraic solution of Bloch equations with time-dependent coefficients

Sergey V. Prants

Physics Letters A•Mar 1, 1990•19 citations

Time-dependent linear Hamiltonian systems and quantum mechanics

Jorge Rezende

Letters in Mathematical Physics•Oct 1, 1996•5 citations

Invariants and Lie algebraic solutions of Schrödinger equation

Franco Salmistraro, Riccardo Rosso

A representation of invariants in quantum mechanics for a general time-dependent Hamiltonian is provided. The main properties of these operators and their relevance for solving the Schrödinger equation are discussed in light of this representation. In particular, the well-known Lewis and Riesenfeld’s method is shown to be recovered quite directly by the present approach. A detailed analysis is concerned with Hamiltonians which at each instant are elements of a finite dimensional Lie algebra. Exploiting the Wei and Norman’s theory for such Hamiltonians, it is found that the evolution of a quantum system is always determined, in part or fully, by an invariant which belongs to the same algebra.

Journal of Mathematical Physics•Sep 1, 1993•8 citations

Time-evolution operator and Lie algebras

Francisco Marcelo Fernández

We discuss the Schr\"odinger equation with a time-dependent Hamiltonian that can be written as a linear combination of operators which span a finite-dimensional Lie algebra. The equations of motion for the operators in the Heisenberg representation are shown to be useful in calculating matrix elements and transition probabilities, as well as in obtaining the time-evolution operator. A general time-dependent one-dimensional bilinear Hamiltonian is considered as an illustrative example, and the product form for the time-evolution operator is shown to be global.

Physical Review A•Jul 1, 1989•38 citations

Exact solutions for time-dependent phenomena in quantum mechanics

M. Kleber

Physics Reports•Jan 1, 1994•155 citations

A generalized coherent state approach of the quantum dynamics for suitable time-dependent hamiltonians

Monique Combescure

Journées Équations aux dérivées partielles•Jan 1, 1992•4 citations
A representation of invariants in quantum mechanics for a general time-dependent Hamiltonian is provided. The main properties of these operators and their relevance for solving the Schrödinger equation are discussed in light of this representation. In particular, the well-known Lewis and Riesenfeld’s method is shown to be recovered quite directly by the present approach. A detailed analysis is concerned with Hamiltonians which at each instant are elements of a finite dimensional Lie algebra. Exploiting the Wei and Norman’s theory for such Hamiltonians, it is found that the evolution of a quantum system is always determined, in part or fully, by an invariant which belongs to the same algebra.
We discuss the Schr\"odinger equation with a time-dependent Hamiltonian that can be written as a linear combination of operators which span a finite-dimensional Lie algebra. The equations of motion for the operators in the Heisenberg representation are shown to be useful in calculating matrix elements and transition probabilities, as well as in obtaining the time-evolution operator. A general time-dependent one-dimensional bilinear Hamiltonian is considered as an illustrative example, and the product form for the time-evolution operator is shown to be global.