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

[摘要] The aim of this thesis is the semi-classical implementation of Wegner's flow equationsand comparison with the well-established Wentzel-Kramers-Brillouin method. We do thisby converting operators, in particular the Hamiltonian, into scalar functions, while anisomorphism with the operator product is maintained by the introduction of the Moyalproduct. A flow equation in terms of these scalar functions is set up and then approximatedby expanding it to first order in ~. We apply this method to two potentials, namely thequartic anharmonic oscillator and the symmetric double-well potential. Results obtainedvia the flow equations are then compared with those obtained from the WKB method.

[发布机构] Stellenbosch University