Use this URL to cite or link to this record in EThOS:
Title: Aspects of PT-symmetric quantum mechanics
Author: Millican-Slater, Adam
ISNI:       0000 0001 3408 006X
Awarding Body: Durham University
Current Institution: Durham University
Date of Award: 2004
Availability of Full Text:
Access from EThOS:
Access from Institution:
PT-symmetric quantum mechanics is an alternative to the usual hermitian quantum mechanics. We will start this thesis by taking an overview of the subject, seeing some of the elementary consequences of this different approach. The main part of the work will be an depth study of a specific Hamiltonian(diagram) This is a generalisation of the well understood harmonic oscillator with angular momentum. By making this generalisation we break the hermiticity of the problem. This leads to some intriguing results. We will be particularly interested in the merging of eigenvalues for M <1.We study the problem using a number of techniques. First the Hamiltonian is studied at the classical level and the behaviour of a particle moving in the corresponding potential is studied. Having seen the consequences at the classical level we return to the quantum case. The Hamiltonian is first solved perturbativly. This method is shown to be valid for PT-symmetric quantum mechanics. It is shown that asymptotic limits of the matrix do not capture the full behaviour of the energy levels. We then move on to study the problem considering techniques arising from the ODE/IM correspondence. Using this approach we are able to give an analytic description of the phenomena and explain the merging of eigenvalues.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available