Kerr, William C.http://hdl.handle.net/10339/259302014-09-03T04:34:27Z2014-09-03T04:34:27ZElectron spin and probability current density in quantum mechanicsHodge, W. B.Migirditch, S. V.Kerr, William C.http://hdl.handle.net/10339/393522014-08-01T08:20:16Z2014-01-01T00:00:00ZElectron spin and probability current density in quantum mechanics
Hodge, W. B.; Migirditch, S. V.; Kerr, William C.
This paper analyzes how the existence of electron spin changes the equation for the probability current density in the quantum-mechanical continuity equation. A spinful electron moving in a potential energy field experiences the spin-orbit interaction, and that additional term in the time-dependent SchrÃ¶dinger equation places an additional spin-dependent term in the probability current density. Further, making an analogy with classical magnetostatics hints that there may be an additional magnetization current contribution. This contribution seems not to be derivable from a non-relativistic time-dependent SchrÃ¶dinger equation, but there is a procedure described in the quantum mechanics textbook by Landau and Lifschitz to obtain it. We utilize and extend their procedure to obtain this magnetization term, which also gives a second derivation of the spin-orbit term. We conclude with an evaluation of these terms for the ground state of the hydrogen atom with spin-orbit interaction. The magnetization contribution is generally the larger one, except very near an atomic nucleus.
2014-01-01T00:00:00ZThermodynamic Venn Diagrams: Sorting Out Forces, Fluxes, and Legendre TransformsKerr, William C.Macosko, Jed C.http://hdl.handle.net/10339/362662011-10-11T17:30:18Z2011-01-01T00:00:00ZThermodynamic Venn Diagrams: Sorting Out Forces, Fluxes, and Legendre Transforms
Kerr, William C.; Macosko, Jed C.
We show how to use a Venn diagram to illuminate the relations among the different thermodynamic potentials, forces, and fluxes of a simple system. A single diagram shows all of the thermodynamic potentials obtainable by Legendre transformations starting from the internal energy as the fundamental potential. From the diagram, we can also read off the Maxwell relations deduced from each of these potentials. We construct a second Venn diagram that shows the analogous information for the Massieu functions, obtained by Legendre transformations starting from the entropy as the fundamental thermodynamic function.
2011-01-01T00:00:00ZApplication of Berry's phase to the effective mass of Bloch electronsKerr, William C.Rave, M. J.http://hdl.handle.net/10339/158802010-11-24T18:24:47Z2009-12-04T16:39:56ZApplication of Berry's phase to the effective mass of Bloch electrons
Kerr, William C.; Rave, M. J.
2009-12-04T16:39:56ZRole of Elastic Compatibility in Martensitic Texture EvolutionKillough, M.Saxena, A.Swart, P.Bishop, A.Kerr, William C.http://hdl.handle.net/10339/160172014-01-17T18:06:55Z2009-10-28T13:27:05ZRole of Elastic Compatibility in Martensitic Texture Evolution
Killough, M.; Saxena, A.; Swart, P.; Bishop, A.; Kerr, William C.
2009-10-28T13:27:05Z