Semiclassical quantization via adiabatic switching. I. Choice of tori and initial conditions for two-dimensional systems

Journal Article · Sat Oct 15 04:00:00 EDT 1988 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.38.3877· OSTI ID:6830635

Zakrzewski, J; Saini, S; Taylor, H S

A general theoretical base and a general strategy for implementing semiclassical quantization using the adiabatic-switching method are presented for two-dimensional systems. The method proposed does not depend on specialized coordinates, trajectory, or surfaces-of-section studies and is generalizable to multidimensional systems. The choice of the initial tori for the switching procedure is accomplished by simple diagonalizations of small-dimensional matrix representations of invariant operators obtained from perturbation theory. The method gives quantum energies at a useful level of accuracy for the vast majority of states in many of the well-known nonresonant and resonant Hamiltonian cases. Many eigenvalues previously thought unobtainable when the adiabatic-switching method is used are obtained in a quite simple manner.

• Research Organization: Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482
• OSTI ID: 6830635
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 38:8; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

640304* -- Atomic
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
ATOMIC IONS
CHARGED PARTICLES
COLLISIONS
CORRELATIONS
CROSS SECTIONS
ELECTRON COLLISIONS
ELECTRON-MOLECULE COLLISIONS
ELEMENTS
ENERGY LEVELS
ENERGY-LEVEL TRANSITIONS
EXCITATION
EXCITED STATES
HEATING
IONIZATION
IONS
MOLECULAR IONS
MOLECULE COLLISIONS
NONMETALS
OXYGEN
PLASMA HEATING
SHOCK HEATING
VIBRATIONAL STATES