QUASI-CLASSICAL THEORY OF THE NON-SPINNING ELECTRON
A modified Hamiltonian-Jacobi theory of classical mechanics following the work of Van VIeck. This modified Hamiltonian-Jacobi theory. or quasi- classical theory, permits an exhibition in elassical mechanies many features that in the past were exclusively associated wlth quantum mechanics. Classical wave functions, classical operators, classical eigenvalue'' equations, a classical ' sum over paths'' formulation of classical mechanies, and classical creation and destruction operators are discussed. Following Van Vleck, the WKB approximate soIutions to the Schrodinger equation can be derived from the solutions of the elassical Hamilton-Jacobi equation. If the methods of Keller are applied to the nonrelativistie and relativistic Kepler problem, eigenvalues are derived from the requirenient of single-valuedness imposed on the WKB soultions. The energy eigenvalues are those given by the Schrodinger equation and the Klein-Gordon equation, respectively. In the particular case of the harmonic oscillator there exists a canonical transformation which transforms the quasiclassical equation into an exact equation of quantum mechanics. It is suggested that if the WKB approximation and the Schrodinger equation predict the same eigenvalues, then there always exists a canonical transformation transforming the quasi-classical equaiion into the corresponding Sehrodinger equatlon. Finally, the quasi- classical equations are derived in momentum space. (auth)
- Research Organization:
- Syracuse Univ., N.Y.
- NSA Number:
- NSA-16-010883
- OSTI ID:
- 4808613
- Journal Information:
- Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Vol. Vol: 125; Other Information: Orig. Receipt Date: 31-DEC-62
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
Similar Records
QUASI-CLASSICAL THEORY OF A RELATIVISTIC SPINNING ELECTRON
Vector fields, line integrals, and the Hamilton-Jacobi equation: Semiclassical quantization of bound states