Quantum equations of motion and the Liouville equation
Journal Article
·
· Found. Phys.; (United States)
Equations of motion for explicitly time-dependent operators in the Heisenberg and Schroedinger pictures, respectively, are reviewed. A simple transformation reduces the related equation in the Heisenberg picture to closed form. An algorithm is introduced for the classical limit which, in either picture, returns the classical equation of motion for dynamical functions. Applications of this algorithm to the equation of motion for the density matrix reduces it to the classical Liouville equation. A property related to this algorithm is established for the commutator of any two analytic functions of finite polynomials of conjugate variables.
- Research Organization:
- Tel-Aviv Univ., Israel
- OSTI ID:
- 5836241
- Journal Information:
- Found. Phys.; (United States), Journal Name: Found. Phys.; (United States) Vol. 17:10; ISSN FNDPA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
645400* -- High Energy Physics-- Field Theory
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGORITHMS
BOLTZMANN-VLASOV EQUATION
CLASSICAL MECHANICS
DENSITY MATRIX
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
FIELD THEORIES
HEISENBERG PICTURE
INVARIANCE PRINCIPLES
MATHEMATICAL LOGIC
MATHEMATICAL OPERATORS
MATRICES
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY
QUANTUM MECHANICS
QUANTUM OPERATORS
SCHROEDINGER PICTURE
TIME DEPENDENCE
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGORITHMS
BOLTZMANN-VLASOV EQUATION
CLASSICAL MECHANICS
DENSITY MATRIX
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
FIELD THEORIES
HEISENBERG PICTURE
INVARIANCE PRINCIPLES
MATHEMATICAL LOGIC
MATHEMATICAL OPERATORS
MATRICES
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY
QUANTUM MECHANICS
QUANTUM OPERATORS
SCHROEDINGER PICTURE
TIME DEPENDENCE