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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

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.