Bifunctionate Solutions to the Schrödinger Equation for Reactive, Three-Atom, Colinear Encounters

Author: Meister, John Joseph

Year: 1973

Degree: Dissertation (Ph.D.)

Advisor: Unknown, Unknown

Committee Member: Unknown, Unknown

Option: Chemistry; Physics

DOI: 10.7907/fhwd-vj37

Abstract

Two methods for solving the Schrödinger equation for one dimensional, three atom, electronically adiabatic, reactive collisions have been investigated. The first bifunctionate method was proposed by Diestler in 1969. It solves for vibrational excitation probabilities by expanding two parts of the total solution to the scattering problem in eigenfunctions of the unperturbed diatoms. These diatoms are the target and product diatoms in the reactive encounter. This formalism allows the eigenfunction series representation of the total solution to decay to zero in the interaction region of the reaction. Proposition 1 shows that this decay process is indicative of a failure in Diestler's method which renders its solutions invalid.

A technique proposed as a means of solving the equations governing nuclear collisions was also investigated. This formalism, called the Method of Subtracted Asymptotics, has been shown to be an application of the general mechanism of eigenfunction expansion to the scattering problem. Because of analysis problems induced by the extensive eigenfunction series demanded by this method, the Method of Subtracted Asymptotics is not an efficient or practical manner of solving the scattering problem. This method is treated in part 2 of this work.

Tests used to varify the numerical accuracy of several studies of the Method of Subtracted Asymptotics required the values of several special functions on the complex plane. To meet these needs, algorithms which compute the value of a complex number raised to a complex power, the Gamma function, the Digamma function and the Hyper geometric function were prepared. These algorithms are discussed and presented in part 1 of this thesis.

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