Abstract:
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) .
