On the path integral formulation and the evaluation of quantum statistical averages

Four problems of physical interest have been solved in this thesis using the path integral formalism. Using the trigonometric expansion method of Burton and de Borde (1955), we found the kernel for two interacting one dimensional oscillators• The result is the same as one would obtain using a normal coordinate transformation, We next introduced the method of Papadopolous (1969), which is a systematic perturbation type method specifically geared to finding the partition function Z, or equivalently, the Helmholtz free energy F, of a system of interacting oscillators. We applied this method to the next three problems considered• First, by summing the perturbation expansion, we found F for a system of N interacting Einstein oscillators^ The result obtained is the same as the usual result obtained by Shukla and Muller (1972) • Next, we found F to 0(Xi)f where A is the usual Tan Hove ordering parameter* The results obtained are the same as those of Shukla and Oowley (1971), who have used a diagrammatic procedure, and did the necessary sums in Fourier space* We performed the work in temperature space• Finally, slightly modifying the method of Papadopolous, we found the finite temperature expressions for the Debyecaller factor in Bravais lattices, to 0(AZ) and u(/K/ j,where K is the scattering vector* The high temperature limit of the expressions obtained here, are in complete agreement with the classical results of Maradudin and Flinn (1963) .

Name thesis:degree_name

M.Sc. Physics

Level thesis:degree_level

Masters

Discipline thesis:degree_discipline

Faculty of Mathematics and Science

Department dc:contributor.department

Department of Physics

Grantor

Brock University

Year dc:date.issued

1979

Author dc:creator

• Manz, Arthur.

• Quantum statistics.
• Quantum theory.
• Feynman integrals.

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/10464/1987

OAI identifier oai:identifier

oai:brocku.scholaris.ca:10464/1987