Generalized Gaussian wave packet dynamics, Schroedinger equation, and stationary phase approximation

Journal Article · Mon Aug 15 04:00:00 EDT 1988 · J. Chem. Phys.; (United States)

OSTI ID:7185265

Huber, D; Heller, E J; Littlejohn, R G

We have recently published a new semiclassical method, generalized Gaussian wave packet dynamics, which extends Gaussian wave packet dynamics into complex phase space. Although we were able to give an accurate formulation of the method, we had at the time of writing that paper only an intuitive, heuristic understanding of the deeper causes which make the method work. A more mathematical understanding was needed. To close this gap we show in this paper the equivalence of the new method with a first order expansion of (h/2..pi..) of the Schroedinger equation. We further prove that the new method is equivalent to the stationary phase approximation, using the usual WKB formula for the propagator. The latter equivalence enables us to show that all the symmetry properties of time-dependent quantum mechanics also hold in the new semiclassical theory. Finally, we provide some elaboration of the method, and clarify several issues that were not discussed before. With this new insight we are able to formulate a simple rule for the calculation of semiclassical wave functions that contain contributions from more than one branch. This corrects for the divergence of semiclassical wave functions near caustics, a problem that we encountered in the preceding paper.

• Research Organization: Department of Chemistry BG-10, University of Washington, Seattle, Washington 98195
• OSTI ID: 7185265
• Journal Information: J. Chem. Phys.; (United States), Journal Name: J. Chem. Phys.; (United States) Vol. 89:4; ISSN JCPSA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL SPACE
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SPACE
QUANTUM MECHANICS
SCHROEDINGER EQUATION
SEMICLASSICAL APPROXIMATION
SPACE
WAVE EQUATIONS
WKB APPROXIMATION