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Physical Sciences and Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

Missouri University of Science and Technology

2016

Hamiltonians

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Full-Text Articles in Physical Sciences and Mathematics

Nonresonant Two-Photon Transitions In Length And Velocity Gauges, Ulrich D. Jentschura Aug 2016

Nonresonant Two-Photon Transitions In Length And Velocity Gauges, Ulrich D. Jentschura

Physics Faculty Research & Creative Works

We reexamine the invariance of two-photon transition matrix elements and corresponding two-photon Rabi frequencies under the "gauge" transformation from the length to the velocity gauge. It is shown that gauge invariance, in the most general sense, only holds at exact resonance, for both one-color as well as two-color absorption. The arguments leading to this conclusion are supported by analytic calculations which express the matrix elements in terms of hypergeometric functions, and ramified by a "master identity" which is fulfilled by off-diagonal matrix elements of the Schrödinger propagator under the transformation from the velocity to the length gauge. The study of …

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Dirac Hamiltonian And Reissner-Nordström Metric: Coulomb Interaction In Curved Space-Time, J. H. Noble, Ulrich D. Jentschura Mar 2016

Dirac Hamiltonian And Reissner-Nordström Metric: Coulomb Interaction In Curved Space-Time, J. H. Noble, Ulrich D. Jentschura

Physics Faculty Research & Creative Works

We investigate the spin-1/2 relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordström space-time geometry and the simultaneous covariant coupling to the central electrostatic field. The relativistic Dirac Hamiltonian for the Reissner-Nordström geometry is derived. A Foldy-Wouthuysen transformation reveals the presence of gravitational and electrogravitational spin-orbit coupling terms which generalize the Fokker precession terms found for the Dirac-Schwarzschild Hamiltonian, and other electrogravitational correction terms to the potential proportional to αnG, where α is the fine-structure constant and …

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