Connections with Bohmian Mechanics
نویسندگان
چکیده
OF THE DISSERTATION Connections with Bohmian Mechanics by James Oliver Taylor Dissertation Director: Sheldon Goldstein We begin by formulating non-relativistic Bohmian mechanics for theories in which the wave functions are sections of a Hermitian vector bundle over a Riemannian manifold. We give geometric interpretations of the Pauli equation and the Dirac equation. We then explain the influence of non-trivial topology in formulating Bohmian theories and use that to explain the quantum story of identical particles. We take a break from Bohmian mechanics briefly to investigate when the covariant derivatives of a mapping between manifolds may be used in a Taylor polynomial fashion in order to find the best polynomial approximation to the map. We finish by first formulating and then giving some results about a new algorithm for computing solutions to Schrödinger’s equation.
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