Fourier transform methods for calculating action variables and semiclassical eigenvalues for coupled oscillator systems

Journal Article · Thu Dec 20 04:00:00 EST 1984 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.447592· OSTI ID:5987136

Eaker, C W; Schatz, G C; De Leon, N; Heller, E J

Two methods for calculating the good action variables and semiclassical eigenvalues for coupled oscillator systems are presented, both of which relate the actions to the coefficients appearing in the Fourier representation of the normal coordinates and momenta. The two methods differ in that one is based on the exact expression for the actions together with the EBK semiclassical quantization condition while the other is derived from the Sorbie--Handy (SH) approximation to the actions. However, they are also very similar in that the actions in both methods are related to the same set of Fourier coefficients and both require determining the perturbed frequencies in calculating actions. These frequencies are also determined from the Fourier representations, which means that the actions in both methods are determined from information entirely contained in the Fourier expansion of the coordinates and momenta. We show how these expansions can very conveniently be obtained from fast Fourier transform (FFT) methods and that numerical filtering methods can be used to remove spurious Fourier components associated with the finite trajectory integration duration. In the case of the SH based method, we find that the use of filtering enables us to relax the usual periodicity requirement on the calculated trajectory. Application to two standard Henon--Heiles models is considered and both are shown to give semiclassical eigenvalues in good agreement with previous calculations for nondegenerate and 1:1 resonant systems. In comparing the two methods, we find that although the exact method is quite general in its ability to be used for systems exhibiting complex resonant behavior, it converges more slowly with increasing trajectory integration duration and is more sensitive to the algorithm for choosing perturbed frequencies than the SH based method.

• Research Organization: Department of Chemistry, Northwestern University, Evanston, Illinois 60201
• OSTI ID: 5987136
• Journal Information: J. Chem. Phys.; (United States), Journal Name: J. Chem. Phys.; (United States) Vol. 81:12; ISSN JCPSA
• Country of Publication: United States
• Language: English

Related Subjects

640305* -- Atomic
Molecular & Chemical Physics-- Atomic & Molecular Theory-- (-1987)
74 ATOMIC AND MOLECULAR PHYSICS
COUPLING
EIGENVALUES
ELECTRONIC EQUIPMENT
EQUIPMENT
FOURIER TRANSFORMATION
INTEGRAL TRANSFORMATIONS
MECHANICS
OSCILLATION MODES
OSCILLATORS
QUANTUM MECHANICS
SEMICLASSICAL APPROXIMATION
TRANSFORMATIONS