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Approximation Methods In Relativistic Eigenvalue Perturbation Theory, Jonathan Howard Noble
Approximation Methods In Relativistic Eigenvalue Perturbation Theory, Jonathan Howard Noble
Doctoral Dissertations
"In this dissertation, three questions, concerning approximation methods for the eigenvalues of quantum mechanical systems, are investigated: (i) What is a pseudo-Hermitian Hamiltonian, and how can its eigenvalues be approximated via numerical calculations? This is a fairly broad topic, and the scope of the investigation is narrowed by focusing on a subgroup of pseudo-Hermitian operators, namely, PT-symmetric operators. Within a numerical approach, one projects a PT-symmetric Hamiltonian onto an appropriate basis, and uses a straightforward two-step algorithm to diagonalize the resulting matrix, leading to numerically approximated eigenvalues. (ii) Within an analytic ansatz, how can a relativistic Dirac Hamiltonian be …