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The Principles of Quantum Mechanics

About: The article was published on 1930-01-01 and is currently open access. It has received 5991 citations till now. The article focuses on the topics: Quantum statistical mechanics & Open quantum system.

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28 Feb 1983
TL;DR: Using classical and quantum methods with a strong emphasis on symmetry principles, the volume as discussed by the authors develops the theory of varied optical activity and related phenomena from the perspective of molecular scattering of polarized light.
Abstract: Ranging from the physics of elementary particles to the structure of viruses, the subject matter of this book stresses the importance of optical activity and chirality in modern science and will be of interest to a wide range of scientists. Using classical and quantum methods with a strong emphasis on symmetry principles, the volume develops the theory of varied optical activity and related phenomena from the perspective of molecular scattering of polarized light. First Edition Hb (1983): 0-521-24602-4

1,543 citations

Journal ArticleDOI
TL;DR: In this paper, the light-cone quantization of quantum field theory has been studied from two perspectives: as a calculational tool for representing hadrons as QCD bound states of relativistic quarks and gluons, and also as a novel method for simulating quantum field theories on a computer.

1,231 citations

Journal ArticleDOI
TL;DR: In this paper, the non-linear optical polarization of an isolated atom or molecule is treated, giving careful consideration to secular and resonant terms in the perturbation expansion, and the Method of Averages introduced by Bogoliubov and Mitropolsky is used.
Abstract: The non-linear optical polarization of an isolated atom or molecule is treated, giving careful consideration to secular and resonant terms in the perturbation expansion. The Method of Averages introduced by Bogoliubov and Mitropolsky is used. The case where resonance-induced excited state populations are negligible, which is relevant to a wide range of non-linear optical experiments, is examined in detail for polarizations through third order in the perturbing fields. This yields concise expressions which are valid for any combination of applied field frequencies, including static fields.

1,184 citations

Journal ArticleDOI
TL;DR: In this article, a review of various methods of deriving expressions for quantum-mechanical quantities in the limit when hslash is small (in comparison with the relevant classical action functions) is presented.
Abstract: We review various methods of deriving expressions for quantum-mechanical quantities in the limit when hslash is small (in comparison with the relevant classical action functions). To start with we treat one-dimensional problems and discuss the derivation of WKB connection formulae (and their reversibility), reflection coefficients, phase shifts, bound state criteria and resonance formulae, employing first the complex method in which the classical turning points are avoided, and secondly the method of comparison equations with the aid of which uniform approximations are derived, which are valid right through the turningpoint regions. The special problems associated with radial equations are also considered. Next we examine semiclassical potential scattering, both for its own sake and also as an example of the three-stage approximation method which must generally be employed when dealing with eigenfunction expansions under semiclassical conditions, when they converge very slowly. Finally, we discuss the derivation of semiclassical expressions for Green functions and energy level densities in very general cases, employing Feynman's path-integral technique and emphasizing the limitations of the results obtained. Throughout the article we stress the fact that all the expressions obtained involve quantities characterizing the families of orbits in the corresponding purely classical problems, while the analytic forms of the quantal expressions depend on the topological properties of these families. This review was completed in February 1972.

1,133 citations

Journal ArticleDOI
TL;DR: The theoretical predictions and the experimental techniques that are most often used for the challenging tasks of visualizing and manipulating these tiny structures are reviewed and the computational approaches taken, including ab initio quantum mechanical simulations, classical molecular dynamics, and continuum models are outlined.
Abstract: Soon after the discovery of carbon nanotubes, it was realized that the theoretically predicted mechanical properties of these interesting structures–including high strength, high stiffness, low density and structural perfection–could make them ideal for a wealth of technological applications. The experimental verification, and in some cases refutation, of these predictions, along with a number of computer simulation methods applied to their modeling, has led over the past decade to an improved but by no means complete understanding of the mechanics of carbon nanotubes. We review the theoretical predictions and discuss the experimental techniques that are most often used for the challenging tasks of visualizing and manipulating these tiny structures. We also outline the computational approaches that have been taken, including ab initio quantum mechanical simulations, classical molecular dynamics, and continuum models. The development of multiscale and multiphysics models and simulation tools naturally arises as a result of the link between basic scientific research and engineering application; while this issue is still under intensive study, we present here some of the approaches to this topic. Our concentration throughout is on the exploration of mechanical properties such as Young’s modulus, bending stiffness, buckling criteria, and tensile and compressive strengths. Finally, we discuss several examples of exciting applications that take advantage of these properties, including nanoropes, filled nanotubes, nanoelectromechanical systems, nanosensors, and nanotube-reinforced polymers. This review article cites 349 references. @DOI: 10.1115/1.1490129#

1,097 citations