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Full-Text Articles in Applied Mathematics
Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang
Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang
Electronic Theses and Dissertations
While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and Paul Loya. In this thesis, we reproduce the Kirsten and Loya approach to …
Electrodynamical Modeling For Light Transport Simulation, Michael G. Saunders
Electrodynamical Modeling For Light Transport Simulation, Michael G. Saunders
Undergraduate Honors Theses
Modernity in the computer graphics community is characterized by a burgeoning interest in physically based rendering techniques. That is to say that mathematical reasoning from first principles is widely preferred to ad hoc, approximate reasoning in blind pursuit of photorealism. Thereby, the purpose of our research is to investigate the efficacy of explicit electrodynamical modeling by means of the generalized Jones vector given by Azzam [1] and the generalized Jones matrix given by Ortega-Quijano & Arce-Diego [2] in the context of stochastic light transport simulation for computer graphics. To augment the status quo path tracing framework with such a modeling …
Isotropic Oscillator Under A Magnetic And Spatially Varying Electric Field, David L. Frost Mr., Frank Hagelberg
Isotropic Oscillator Under A Magnetic And Spatially Varying Electric Field, David L. Frost Mr., Frank Hagelberg
Undergraduate Honors Theses
We investigate the energy levels of a particle confined in the isotropic oscillator potential with a magnetic and spatially varying electric field. Here we are able to exactly solve the Schrodinger equation, using matrix methods, for the first excited states. To this end we find that the spatial gradient of the electric field acts as a magnetic field in certain circumstances. Here we present the changes in the energy levels as functions of the electric field, and other parameters.
A Numerical Model For Nonadiabatic Transitions In Molecules, Devanshu Agrawal
A Numerical Model For Nonadiabatic Transitions In Molecules, Devanshu Agrawal
Undergraduate Honors Theses
In molecules, electronic state transitions can occur via quantum coupling of the states. If the coupling is due to the kinetic energy of the molecular nuclei, then electronic transitions are best represented in the adiabatic frame. If the coupling is instead facilitated through the potential energy of the nuclei, then electronic transitions are better represented in the diabatic frame. In our study, we modeled these latter transitions, called ``nonadiabatic transitions.'' For one nuclear degree of freedom, we modeled the de-excitation of a diatomic molecule. For two nuclear degrees of freedom, we modeled the de-excitation of an ethane-like molecule undergoing cis-trans …