Phd records
https://feeds.library.caltech.edu/people/Meister-John-Joseph/Phd.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 31 Jan 2024 19:27:21 +0000Bifunctionate Solutions to the SchrÃ¶dinger Equation for Reactive, Three-Atom, Colinear Encounters
https://resolver.caltech.edu/CaltechTHESIS:01312018-092115580
Authors: {'items': [{'id': 'Meister-John-Joseph', 'name': {'family': 'Meister', 'given': 'John Joseph'}}]}
Year: 1973
DOI: 10.7907/fhwd-vj37
<p>Two methods for solving the SchrÃ¶dinger 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.</p>
<p>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.</p>
<p>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.</p>https://thesis.library.caltech.edu/id/eprint/10659