Properties of vibrational energy levels in the quasi periodic and stochastic regimes

Journal Article · Sun Jun 01 00:00:00 EDT 1980 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.439075· OSTI ID:5338419

Noid, D W; Koszykowski, M L; Tabor, M; Marcus, R A

Several aspects of the quantal energy spectrum are explored for the Henon--Heiles Hamiltonian system: a striking and initially unexpected continuation of sequences of eigenvalues from the quasiperiodic to the stochastic regime, the origin of large second differences ..delta../sup 2/E/sub i/ of eigenvalues arising from variation of a parameter, the comparison of classical and quantal spectra, and a comparison of the ''classical'' and quantal number of states. In the study of the second differences we find both ''crossings'' and ''avoided crossings'' of the eigenvalues. We discuss the importance of overlapping avoided crossings as a basis for a possible theory of ''quantum stochasticity''.

• Research Organization: Oak Ridge National Laboratory, Oak Ridge, Tennessee 37870
• OSTI ID: 5338419
• Journal Information: J. Chem. Phys.; (United States), Journal Name: J. Chem. Phys.; (United States) Vol. 72:11; ISSN JCPSA
• Country of Publication: United States
• Language: English

Related Subjects

640300* -- Atomic
Molecular & Chemical Physics
74 ATOMIC AND MOLECULAR PHYSICS
EIGENVALUES
ENERGY LEVELS
EXCITED STATES
FUNCTIONS
HAMILTONIAN FUNCTION
MECHANICS
QUANTUM MECHANICS
STOCHASTIC PROCESSES
VIBRATIONAL STATES