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Physical Review

Currents as Coordinates in Nonrelativistic Quantum Mechanics

WILLIAM J. PARDEE, Leonard Schlessinger, Jon Wright

Published Nov 25, 1968• 11 citations
Publisher

Abstract

The formulation of nonrelativistic quantum mechanics using currents and densities as coordinates is investigated. A general solution for a single-particle theory is presented, and several many-body problems are discussed.
DOI
10.1103/physrev.175.2140

Related papers

Nonrelativistic Quantum Mechanics Formulated in Terms of Currents

David J. Gross

The nonrelativistic quantum mechanics of interacting spinless bosons or fermions is formulated in terms of particle and current densities. Natural physical requirements on the structure of the physical states allow one to construct explicitly the physical Hilbert space, and to construct annihilation and creation operators for either bosons or fermions. The problem of extending such methods to the relativistic case is discussed.

Physical Review•Jan 25, 1969•9 citations

Nonlocal Currents as Coordinates for Particles

Josip Z. Soln

We investigate the possibility of formulating the dynamical theories in terms of nonlocal "currents." As an example, we formulate the nonrelativistic system of $n$ identical particles (with and without spin). From these models we learn that the extension to relativistic systems is possible. This is illustrated by treating the Thirring model in terms of nonlocal currents.

Physical Review•Jul 25, 1968•3 citations

A Condensed Course of Quantum Mechanics

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This book represents a concise summary of nonrelativistic quantum mechanics for physics students at the university level. The text covers essential topics, from general mathematical formalism to specific applications. The formulation of quantum theory is explained and supported with illustrations of the general concepts of elementary quantum systems. In addition to traditional topics of nonrelativistic quantum mechanics - including single-particle dynamics, symmetries, semiclassical and perturbative approximations, density-matrix formalism, scattering theory, and the theory of angular momentum - the book also covers modern issues, among them quantum entanglement, decoherence, measurement, nonlocality, and quantum information. Historical context and chronology of basic achievements is also outlined in explanatory notes. Ideal as a supplement to classroom lectures, the book can also serve as a compact and comprehensible refresher of elementary quantum theory for more advanced students.

Karolinum Press eBooks•Jun 1, 2015•0 citations

Density-matrix formulation ofab initiomethods of nonrelativistic quantum mechanics

Antonio Redondo

A density-matrix formulation of the ab initio methods of nonrelativistic quantum mechanics is presented. The variational equations for the standard calculational techniques of molecular quantum mechanics are derived from a single expression for the total energy of an N-particle system. A generalization of the Hohenberg-Kohn theorem is proved, showing that the ground-state energy of a many-body Hamiltonian is a functional of the single-particle density matrix and hence of the first-order reduced-density function (the diagonal of which is the particle density of the standard theorem). The theorem is used to develop a new method to calculate the total energy and single-particle properties of the many-body problem.

Physical Review A•May 1, 1989•6 citations

On a New Form of Quantum Mechanics

Natalia N. Gorobey, Alexander S. Lukyanenko

We propose a new form of nonrelativistic quantum mechanics which is based on a quantum version of the action principle.

arXiv:0807.3508•Jul 22, 2008•0 citations

Transverse current density in nonrelativistic quantum mechanics

Ole Keller

We have seen that the source domain of a transverse photon, a quantum physical object described in this book via the transverse part of the vector potential (AT (r, t)), may be identified with the transverse part of the charged-particle current density (JT (r, t)). In general, many-body quantum physics is needed to determine JT (r, t). However, it is possible to illustrate a number of important principles related to the characterization of the photon source domain by limiting oneself to a study of the single-particle (electron) current density concept in nonrelativistic quantum mechanics.

CRC Press eBooks•May 13, 2014•0 citations
We investigate the possibility of formulating the dynamical theories in terms of nonlocal "currents." As an example, we formulate the nonrelativistic system of nnn identical particles (with and without spin). From these models we learn that the extension to relativistic systems is possible. This is illustrated by treating the Thirring model in terms of nonlocal currents.
This book represents a concise summary of nonrelativistic quantum mechanics for physics students at the university level. The text covers essential topics, from general mathematical formalism to specific applications. The formulation of quantum theory is explained and supported with illustrations of the general concepts of elementary quantum systems. In addition to traditional topics of nonrelativistic quantum mechanics - including single-particle dynamics, symmetries, semiclassical and perturbative approximations, density-matrix formalism, scattering theory, and the theory of angular momentum - the book also covers modern issues, among them quantum entanglement, decoherence, measurement, nonlocality, and quantum information. Historical context and chronology of basic achievements is also outlined in explanatory notes. Ideal as a supplement to classroom lectures, the book can also serve as a compact and comprehensible refresher of elementary quantum theory for more advanced students.
A density-matrix formulation of the ab initio methods of nonrelativistic quantum mechanics is presented. The variational equations for the standard calculational techniques of molecular quantum mechanics are derived from a single expression for the total energy of an N-particle system. A generalization of the Hohenberg-Kohn theorem is proved, showing that the ground-state energy of a many-body Hamiltonian is a functional of the single-particle density matrix and hence of the first-order reduced-density function (the diagonal of which is the particle density of the standard theorem). The theorem is used to develop a new method to calculate the total energy and single-particle properties of the many-body problem.
We have seen that the source domain of a transverse photon, a quantum physical object described in this book via the transverse part of the vector potential (AT (r, t)), may be identified with the transverse part of the charged-particle current density (JT (r, t)). In general, many-body quantum physics is needed to determine JT (r, t). However, it is possible to illustrate a number of important principles related to the characterization of the photon source domain by limiting oneself to a study of the single-particle (electron) current density concept in nonrelativistic quantum mechanics.