Physical Sciences and Mathematics Commons^™

Perspectives On Determinism In Quantum Mechanics: Born, Bohm, And The “Quantal Newtonian” Laws, Viraht Sahni

Publications and Research

Quantum mechanics has a deterministic Schrödinger equation for the wave function. The Göttingen–Copenhagen statistical interpretation is based on the Born Rule that interprets the wave function as a “probability amplitude.” A precept of this interpretation is the lack of determinism in quantum mechanics. The Bohm interpretation is that the wave function is a source of a field experienced by the electrons, thereby attributing determinism to quantum theory. In this paper, we present a new perspective on such determinism. The ideas are based on the equations of motion or “Quantal Newtonian” Laws obeyed by each electron. These Laws, derived from …

The 'Quantal Newtonian' First Law: A Complementary Perspective To The Stationary-State Quantum Theory Of Electrons, Viraht Sahni

Publications and Research

A complementary perspective to the Göttingen-Copenhagen interpretation of stationary-state quantum theory of electrons in an electromagnetic field is described. The perspective, derived from Schrödinger-Pauli theory, is that of the individual electron via its equation of motion or ‘Quantal Newtonian’ First Law. The Law is in terms of ‘classical’ fields experienced by each electron: the sum of the external and internal fields vanishes. The external field is a sum of the electrostatic and Lorentz fields. The internal field is a sum of fields’ representative of Pauli and Coulomb correlations; kinetic effects; electron density; and internal magnetic component. The energy is obtained …

Perspectives On Determinism In Quantum Mechanics: Born, Bohm, And The 'Quantal Newtonian' Laws, Viraht Sahni

Publications and Research

Quantum mechanics has a deterministic Schrödinger equation for the wave function. The Göttingen-Copenhagen statistical interpretation is based on the Born Rule that interprets the wave function as a ‘probability amplitude’. A precept of this interpretation is the lack of determinism in quantum mechanics. The Bohm interpretation is that the wave function is a source of a field experienced by the electrons, thereby attributing determinism to quantum theory. In this paper we present a new perspective on such determinism. The ideas are based on the equations of motion or ‘Quantal Newtonian’ Laws obeyed by each electron. These Laws, derived from the …

A Gauge Theoretic Treatment Of Rovibrational Motion In Diatoms, Gregory Colarch

UNLV Theses, Dissertations, Professional Papers, and Capstones

The Born-Oppenheimer approximation has long been the standard approach to solving the Schrödinger equation for diatomic molecules. In it, nuclear and electronic motions are separated into "slow" and "fast" degrees of freedom and couplings between the two are ignored. The neglect of non-adiabatic couplings leads to an incomplete description of diatomic motion, and in a more refined approach, non-adiabatic couplings are uncoupled by transforming the angular momentum of the molecule and electrons into the body-fixed frame.

In this thesis we examine a "modern" form of the Born-Oppenheimer approximation by exploiting a gauge theoretic approach in a description of molecular motion. …

Reactive Quantum Scattering In Two Dimensions, Roy S. Calfas

Theses and Dissertations

In an effort to develop a more efficient time dependent approach for calculating scattering matrix elements, absorbing boundary conditions are combined together with the channel packet method. As an introduction to scattering, scattering matrix elements are presented for a one-dimensional square well and a one-dimensional potential consisting of a Gaussian well with symmetric Gaussian barriers. Next, the combination of the channel packet method together with absorbing boundary conditions yields an order of magnitude savings in the time necessary to compute the correlation function for the collinear H+H

Ionization Of Rydberg Wave Packets By Subpicosecond, Half-Cycle Electromagnetic Pulses, C. Raman, C. W. S. Conover, C. I. Sukenik, P. H. Bucksbaum

Physics Faculty Publications

We have studied the ionization of Rydberg wave packets by subpicosecond, nearly unipolar electromagnetic field pulses, in the regime where the duration of the electric field is less than the classical Kepler orbit time 2n3 for the wave packet. In contrast to the subpicosecond optical pulses, subpicosecond field pulses can ionize wave packets when the probability density near the inner turning point of the Kepler orbit is low. The transfer of energy from the electromagnetic field to essentially free electrons demonstrates that the pulses are substantially shorter than one field cycle. Such half-cycle pulses can track the wave packet throughout …

Measurement Of Hyperfine Coupling Constants Of The 5d²D₃/₂ And 5d²D₅/₂ Levels In Atomic Cesium Using Polarization Quantum Beat Spectroscopy, Wo Yei

Physics Theses & Dissertations

Accurate measurements of hyperfine constants have revealed effects that can not be explained by a simple hydrogenic picture of the alkali atoms such as cesium [1-3]. More precise experimental results and theoretical treatments are in demand for the alkali elements, especially for atomic cesium because of its wide range of applications. Therefore, it is essential to understand its atomic and nuclear structure. Precision measurement of its excited-states properties such as hyperfine structure provides global information on nuclear charge and current distributions and also serves as a check to the theory and a calibration of calculated excited state wave functions. Accurate …