Semiclassical quantization of nonseparable systems

Journal Article · Sun Apr 01 04:00:00 EST 1979 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.524125· OSTI ID:6456178

Klein, A; Li, C

The problem of semiclassical quantization of nonseparable systems with a finite number of degrees of freedom is studied within the framework of Heisenberg matrix mechanics, in extension of previous work on one-dimensional systems. The relationship between the quantum theory and multiply-periodic classical motions is derived anew. A suitably averaged Lagrangian provides a variational basis not only for the Fourier components of the semiclassical equations of motion, but also for the general definition of action variables. A Legendre transformation to the Hamiltonian verifies that these have been properly chosen and therefore provide a basis for the quantization of nonseparable systems. The problem of connection formulas is discussed by a method integral to the present approach. The action variables are shown to be adiabatic invariants of the classical system. An elementary application of the method is given. The methods of this paper are applicable to nondegenerate systems only.

• Research Organization: Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19174
• OSTI ID: 6456178
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 20:4; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ADIABATIC INVARIANCE
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
FOURIER ANALYSIS
FUNCTIONS
HEISENBERG PICTURE
LAGRANGIAN FUNCTION
MATRIX ELEMENTS
MECHANICS
QUANTUM MECHANICS
VARIATIONAL METHODS
WKB APPROXIMATION