(Stellenbosch : University of Stellenbosch, 2006-12) Thom, Jacobus Daniel; Scholtz, Frederik G.; Geyer, H. B.; University of Stellenbosch. Faculty of Science. Dept. of Physics.
The aim of this thesis is the semi-classical implementation of Wegner’s flow equations
and comparison with the well-established Wentzel-Kramers-Brillouin method. We do this
by converting operators, in particular the Hamiltonian, into scalar functions, while an
isomorphism with the operator product is maintained by the introduction of the Moyal
product. A flow equation in terms of these scalar functions is set up and then approximated
by expanding it to first order in ~. We apply this method to two potentials, namely the
quartic anharmonic oscillator and the symmetric double-well potential. Results obtained
via the flow equations are then compared with those obtained from the WKB method.