A Gauge-Invariant Energy Variational Principle Application to Anisotropic Excitons in High Magnetic Fields

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A new method is developed for treating atoms and molecules in a magnetic field in a gauge-invariant way using the Rayleigh-Ritz energy variational principle. The energy operator depends on the vector potential which must be chosen in some gauge. In order to adapt the trial wave function to the gauge of the vector potential, the trial wave function can be multiplied by a phase factor which depends on the spatial coordinates. When the energy expectation value is minimized with respect to the phase function, the equation for charge conservation for stationary states is obtained. This equation can be solved for ... continued below

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x, 183 leaves : ill.

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Kennedy, Paul K. (Paul Kevin) December 1983.

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  • Kennedy, Paul K. (Paul Kevin)

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A new method is developed for treating atoms and molecules in a magnetic field in a gauge-invariant way using the Rayleigh-Ritz energy variational principle. The energy operator depends on the vector potential which must be chosen in some gauge. In order to adapt the trial wave function to the gauge of the vector potential, the trial wave function can be multiplied by a phase factor which depends on the spatial coordinates. When the energy expectation value is minimized with respect to the phase function, the equation for charge conservation for stationary states is obtained. This equation can be solved for the phase function, and the solution used in the energy expectation value to obtain a gauge-invariant energy. The method is applicable to all quantum mechanical systems for which the variational principle can be applied. It ensures satisfaction of the charge conservation condition, a gauge-invariant energy, and the best upper bound to the ground-state energy which can be obtained for the form of trial wave function chosen.

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x, 183 leaves : ill.

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  • December 1983

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  • Aug. 22, 2014, 6 p.m.

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Kennedy, Paul K. (Paul Kevin). A Gauge-Invariant Energy Variational Principle Application to Anisotropic Excitons in High Magnetic Fields, dissertation, December 1983; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc331501/: accessed November 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .