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Full-Text Articles in Physics
Diabatic And Adiabatic Representations For Atomic Collision Processes, John B. Delos, W. R. Thorson
Diabatic And Adiabatic Representations For Atomic Collision Processes, John B. Delos, W. R. Thorson
Arts & Sciences Articles
ABSTRACT A consistent general definition of diabatic representations has not previously been given, even though many practical examples of such representations have been constructed for specific problems. Such a definition is provided in this paper. Beginning with a classical trajectory formulation, we describe the form and behavior of velocity‐dependent couplings in slow collisions, including the effects of electron‐translation factors (ETF’s). We compare the couplings arising from atomic representations and atomic ETF’s with those arising from molecular representations and ’’switching function’’ ETF’s. We show that a unique set of switching functions makes the two descriptions identical in their effects. We then …
Semiclassical Calculations Of Vibrational Energy Levels For Non-Separable Systems Using The Birkhoff-Gustavson Normal Form, Randall T. Swimm, John B. Delos
Semiclassical Calculations Of Vibrational Energy Levels For Non-Separable Systems Using The Birkhoff-Gustavson Normal Form, Randall T. Swimm, John B. Delos
Arts & Sciences Articles
We present a semiclassical method of calculating vibrational energy levels for a system of nonseparable coupled oscillators. For a Hamiltonian written as a power series in which the leading terms are given by a sum of one‐dimensional harmonic oscillator Hamiltonians, the method involves transforming the original classical Hamiltonian via a succession of canonical transformations into a normal form which is a power series originally defined by Birkhoff and later generalized by Gustavson. Two cases are distinguished. If the harmonic oscillator frequencies in the unperturbed Hamiltonian are incommensurable, then the normal form is a power series whose terms are products of …