WKB approximation for general matrix Hamiltonians
We present a method of obtaining WKB-type solutions for generalized Schroedinger equations for which the Hamiltonian is an arbitrary matrix function of any number of pairs of canonical operators. Our solution reduces the problem to that of finding the matrix which diagonalizes the classical Hamiltonian and determining the scalar WKB wave functions for the diagonalized Hamiltonian's entries (presented explicitly in terms of classical quantities). If the classical Hamiltonian has degenerate eigenvalues, the solution contains a vector in the classically degenerate subspace. This vector satisfies a classical equation and is given explicitly in terms of the classical Hamiltonian as a Dyson series. As an example, we obtain, from the Dirac equation for an electron with anomalous magnetic moment, the relativistic spin-precession equation.
- Research Organization:
- Stanford Linear Accelerator Center, Stanford University, Stanford, California 94305
- DOE Contract Number:
- AC03-76SF00515
- OSTI ID:
- 6497410
- Journal Information:
- Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 23:10; ISSN PRVDA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CLASSICAL MECHANICS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
DYSON REPRESENTATION
EIGENVALUES
EQUATIONS
FUNCTIONS
HAMILTONIANS
MAGNETIC MOMENTS
MATHEMATICAL OPERATORS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
SCHROEDINGER EQUATION
WAVE EQUATIONS
WAVE FUNCTIONS
WKB APPROXIMATION