A flow equation approach to semi-classical approximations : a comparison with the WKB method

Thom, Jacobus Daniel (2006-12)

Thesis (MSc (Physics))--University of Stellenbosch, 2006.

Thesis

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.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/2405
This item appears in the following collections: