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The Classical Limit of Quantum Mechanics

Description: The Feynman path integral formulation of quantum mechanics is a path integral representation for a propagator or probability amplitude in going between two points in space-time. The wave function is expressed in terms of an integral equation from which the Schrodinger equation can be derived. On taking the limit h — 0, the method of stationary phase can be applied and Newton's second law of motion is obtained. Also, the condition the phase vanishes leads to the Hamilton - Jacobi equation. The secondary objective of this paper is to study ways of relating quantum mechanics and classical mechanics. The Ehrenfest theorem is applied to a particle in an electromagnetic field. Expressions are found which are the hermitian Lorentz force operator, the hermitian torque operator, and the hermitian power operator.
Date: December 1977
Creator: Hefley, Velton Wade

Measurement of the Rate Coefficients for the Bimolecular and Termolecular Charge Transfer Reactions of He₂⁺ with Ne, Ar, N₂, CO, CO₂, and CH₄

Description: The problem with which this investigation is concerned is that of measuring the rate coefficients for termolecular charge transfer reactions of He2+ in atmospheric pressure afterglows with the minority reacting species. Of particular interest was the discovery that the presence of a third body can change an improbable charge transfer reaction involving He+2 into a very probable one, as in the case of the reaction with argon. For example, in Tables II and II it was shown that less than a 300 torr pressure of helium was required to double the effective rate of reaction of argon with He2+ while over 3000 torr was required for CH4. The sensitivity of the method has been sufficient to detect termolecular components as small as 2 x 10-30 cm /sec and values were found to range widely from 2 x 10 for Ne to 67 x 10-30 cm6/sec for CO2. The size of these termolecular rates not only served to explain specific anomalous efficiencies of the charge transfer process observed in atmospheric pressure lasers but also suggested the general importance of three-body ion-molecule reactions in higher pressure plasmas.
Date: May 1977
Creator: Lee, Francis Wha-Pyo

Target Thickness Dependence of Cu K X-Ray Production for Ions Moving in Thin Solid Cu Targets

Description: Measurements of the target thickness dependence of the target x-ray production yield for incident fast heavy ions are reported for thin solid Cu targets as a function of both incident projectile atomic number and energy. The incident ions were F, Al, Si, S, and CI. The charge state of the incident ions was varied in each case to study the target x-ray production for projectiles which had an initial charge state, q, of q = Z₁, q = Z₁ - 1, and q < Z₁ - 1 for F, Al, Si, and S ions and q = Z₁ - 1 and q < Z₁ - 1 for C1 ions. The target thicknesses ranged from 2 to 183 ug/cm². In each case the Cu K x-ray yield exhibits a complex exponential dependence on target thickness. A two-component model which includes contributions to the target x-ray production due to ions with 0 and 1 K vacancies and a three-component model which includes contributions due to ions with 0, 1, and 2 K vacancies are developed to describe the observed target K x-ray yields. The two-component model for the C1 data and the three-component model for the F, Al, Si, S, and C1 data are fit to the individual data for each projectile, and the cross sections for both the target and projectile are determined. The fits to the target x-ray data give a systematic representation of the processes involved in x-ray production for fast heavy ions incident on thin solid targets.
Date: December 1977
Creator: Gardner, Raymond K.