Time dependence, complex scaling, and the calculation of resonances in many-electron systems. [Wave functions, energies, widths]

Journal Article · Sun Oct 01 00:00:00 EDT 1978 · Int. J. Quant. Chem.; (United States)

DOI:https://doi.org/10.1002/qua.560140411· OSTI ID:6335489

Nicolaides, C A; Beck, D R

The theory deals with certain aspects of the formal properties of atomic and molecular highly excited nonstationary states and the problem of calculating their wave functions, energies, and widths. The conceptual framework is a decay theory based on the consistent definition and calculation of the t = 0 localized state, vertical bar psi/sub 0/>. Given this framework, the following topics are treated: The variational calculation of psi/sub 0/ and E/sub 0/ using a previously published theory that generalized the projection operator approach to many-electron systems. The exact definition of the resonance energy. The possibility of bound states in the continuum. The relation of psi/sub 0/ to the resonance (Gamow) function psi and of the Hamiltonian to the rotated Hamiltonian H(theta) based on the notion of perturbation of boundary conditions in the asymptotic region. The variational calculation of real and complex energies employing matrix elements of H and H/sup 2/ with square-integrable and resonance functions. The mathematical structure of the time evolution of vertical bar psi/sub 0/> and the possibility of observing nonexponential decays in certain autoionizing states that are very close to the ionization threshold. A many-body theory of atomic and molecular resonances that employs the coordinate rotation method. 107 references.

• Research Organization: Theoretical Chemistry Inst., Athens, Greece
• OSTI ID: 6335489
• Journal Information: Int. J. Quant. Chem.; (United States), Vol. 14:4
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ATOMS
ENERGY LEVELS
MOLECULES
AUTOIONIZATION
BOUND STATE
BOUNDARY CONDITIONS
COORDINATES
DISTURBANCES
ENERGY
ENERGY-LEVEL TRANSITIONS
HAMILTONIANS
INTEGRALS
LEVEL WIDTHS
MANY-BODY PROBLEM
MATRIX ELEMENTS
PROJECTION OPERATORS
RESONANCE
ROTATION
SCALE INVARIANCE
TIME DEPENDENCE
VARIATIONAL METHODS
WAVE FUNCTIONS
FUNCTIONS
INVARIANCE PRINCIPLES
IONIZATION
MATHEMATICAL OPERATORS
MOTION
QUANTUM OPERATORS
640305* - Atomic
Molecular & Chemical Physics- Atomic & Molecular Theory- (-1987)