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

arXiv:1503.07819 · Physics Letters A

On the correspondence between quantum and classical variational principles

D. E. Ruiz, I. Y. Dodin

Published Jun 13, 2015• 15 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2015.06.014

Related papers

Invariant Tori and Heisenberg Matrix Mechanics: A New Window on the Quantum- Classical Correspondence

William R. Greenberg, Abraham Klein, Ching‐Teh Li

Despite the seminal connection between classical multiply periodic motion and Heisenberg matrix mechanics, we show that there are fundamental, previously undisclosed aspects of this quantum-classical correspondence. These include a quantum variational principle that implies the classical variational principle for invariant tori and the connection between commutation relations and quantization of action variables. Possible applications are described briefly.

Physical Review Letters•Aug 14, 1995•27 citations

On the theory of variational principles in quantum mechanics

Giacomo Fonte

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B•Aug 1, 1986•4 citations

Geometry and symmetry of quantum and classical-quantum variational principles

Esther Bonet-Luz, Cesare Tronci

This paper presents the geometric setting of quantum variational principles and extends it to comprise the interaction between classical and quantum degrees of freedom. Euler-Poincaré reduction theory is applied to the Schrödinger, Heisenberg, and Wigner-Moyal dynamics of pure states. This construction leads to new variational principles for the description of mixed quantum states. The corresponding momentum map properties are presented as they arise from the underlying unitary symmetries. Finally, certain semidirect-product group structures are shown to produce new variational principles for Dirac’s interaction picture and the equations of hybrid classical-quantum dynamics.

arXiv:1501.07202•Journal of Mathematical Physics•Aug 1, 2015•21 citations

ON THE VARIATIONAL PRINCIPLES OF QUANTUM MECHANICS

Guy Rideau

Compt. rend.•Dec 21, 1953•0 citations

A variational principle for quantum mechanics

H.H. Rosenbrock

Physics Letters A•Aug 1, 1985•28 citations

Variational Principle in the Quantum Statistical Theory

É. A. Arinshtein

In the present paper, a generalization of the method of partial summation of the expansion of the thermodynamical potential is proposed. This generalization allows one to obtain the corresponding equations for higher-order correlation matrices, as well as to formulate the variational method for their solution. We show that correlation matrices of equilibrium quantum system satisfy a variational principle for thermodynamic potential which is functional of these matrices that provides a thermodynamic consistency of the theory. This result is similar to a variational principle for correlation functions of classical systems.

Journal of Modern Physics•Jan 1, 2014•2 citations
This paper presents the geometric setting of quantum variational principles and extends it to comprise the interaction between classical and quantum degrees of freedom. Euler-Poincaré reduction theory is applied to the Schrödinger, Heisenberg, and Wigner-Moyal dynamics of pure states. This construction leads to new variational principles for the description of mixed quantum states. The corresponding momentum map properties are presented as they arise from the underlying unitary symmetries. Finally, certain semidirect-product group structures are shown to produce new variational principles for Dirac’s interaction picture and the equations of hybrid classical-quantum dynamics.
In the present paper, a generalization of the method of partial summation of the expansion of the thermodynamical potential is proposed. This generalization allows one to obtain the corresponding equations for higher-order correlation matrices, as well as to formulate the variational method for their solution. We show that correlation matrices of equilibrium quantum system satisfy a variational principle for thermodynamic potential which is functional of these matrices that provides a thermodynamic consistency of the theory. This result is similar to a variational principle for correlation functions of classical systems.