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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 …