Browsing by Author "Pierce, John Festus"
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Item A two-state analysis of the one-dimensional relativistic particle(1967) Pierce, John Festus; Kiehn, R. M.; Walker, Robert H.; Rich, David C.The quantum description of a one-dimensional relativistic particle can be formulated in terms of a Feynman two-state analysis. The formalism presents the main physical features of the relativistic particle in a concise, simple form. A Hamiltonian is developed in analogy with the ammonia molecule in an electric field. Using this Hamiltonian the conditions under which a particle loses its positive definite energy quality can be determined. Zitterbewegung, the Klein paradox, and the symmetry between particles of negative energy and positive energy anti-particles can be developed as a consequence of this condition. A second order propagation equation for the state vector is formulated which may be interpreted in two ways: (1) the state space is flat and the state vectors satisfy a Feynman Gell-Mann propagation equation; (2) the state vectors satisfy a Klein Gordon equation, but the state space is structured or curved. The structure of the manifold, given by a Weyl geometry, is due to the presence of an electromagnetic field.Item Existence and uniqueness in the finite elastostatic Dirichlet problem(1973) Pierce, John Festus; Kiehn, R. M.; Allred, John C.; Collins, R. Eugene; Walker, Robert H.; Whitman, Andrew P.A qualitative model for the finite elastostatic Dirichlet problem is presented. The principal feature is that the solution space is a differentiable manifold as opposed to a topological vector space. The nature of the solution manifold reflects the imposed boundary condition the body topology, and varies with them. The model permits one to utilize contemporary mathematical methods to resolve existence and uniqueness questions.