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Classical Systems in Quantum Mechanics

2020-06-23 Science
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Release : 2020-06-23
Genre : Science
Kind : eBook
Book Rating : 708/5 ( reviews)

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Book Synopsis Classical Systems in Quantum Mechanics by : Pavel Bóna

Download or read book Classical Systems in Quantum Mechanics written by Pavel Bóna. This book was released on 2020-06-23. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates two possibilities for describing classical-mechanical physical systems along with their Hamiltonian dynamics in the framework of quantum mechanics.The first possibility consists in exploiting the geometrical properties of the set of quantum pure states of "microsystems" and of the Lie groups characterizing the specific classical system. The second approach is to consider quantal systems of a large number of interacting subsystems – i.e. macrosystems, so as to study the quantum mechanics of an infinite number of degrees of freedom and to look for the behaviour of their collective variables. The final chapter contains some solvable models of “quantum measurement" describing dynamical transitions from "microsystems" to "macrosystems".

Chaos in Classical and Quantum Mechanics

2013-11-27 Mathematics
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Release : 2013-11-27
Genre : Mathematics
Kind : eBook
Book Rating : 838/5 ( reviews)

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Book Synopsis Chaos in Classical and Quantum Mechanics by : Martin C. Gutzwiller

Download or read book Chaos in Classical and Quantum Mechanics written by Martin C. Gutzwiller. This book was released on 2013-11-27. Available in PDF, EPUB and Kindle. Book excerpt: Describes the chaos apparent in simple mechanical systems with the goal of elucidating the connections between classical and quantum mechanics. It develops the relevant ideas of the last two decades via geometric intuition rather than algebraic manipulation. The historical and cultural background against which these scientific developments have occurred is depicted, and realistic examples are discussed in detail. This book enables entry-level graduate students to tackle fresh problems in this rich field.

The Transition to Chaos

2013-04-17 Science
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Release : 2013-04-17
Genre : Science
Kind : eBook
Book Rating : 521/5 ( reviews)

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Book Synopsis The Transition to Chaos by : Linda Reichl

Download or read book The Transition to Chaos written by Linda Reichl. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: resonances. Nonlinear resonances cause divergences in conventional perturbation expansions. This occurs because nonlinear resonances cause a topological change locally in the structure of the phase space and simple perturbation theory is not adequate to deal with such topological changes. In Sect. (2.3), we introduce the concept of integrability. A sys tem is integrable if it has as many global constants of the motion as degrees of freedom. The connection between global symmetries and global constants of motion was first proven for dynamical systems by Noether [Noether 1918]. We will give a simple derivation of Noether's theorem in Sect. (2.3). As we shall see in more detail in Chapter 5, are whole classes of systems which are now known to be inte there grable due to methods developed for soliton physics. In Sect. (2.3), we illustrate these methods for the simple three-body Toda lattice. It is usually impossible to tell if a system is integrable or not just by looking at the equations of motion. The Poincare surface of section provides a very useful numerical tool for testing for integrability and will be used throughout the remainder of this book. We will illustrate the use of the Poincare surface of section for classic model of Henon and Heiles [Henon and Heiles 1964].

Geometric Formulation of Classical and Quantum Mechanics

2011 Science
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Release : 2011
Genre : Science
Kind : eBook
Book Rating : 726/5 ( reviews)

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Book Synopsis Geometric Formulation of Classical and Quantum Mechanics by : G. Giachetta

Download or read book Geometric Formulation of Classical and Quantum Mechanics written by G. Giachetta. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. This book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations.

Classical Dynamics of Particles and Systems

2013-10-22 Science
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Release : 2013-10-22
Genre : Science
Kind : eBook
Book Rating : 818/5 ( reviews)

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Book Synopsis Classical Dynamics of Particles and Systems by : Jerry B. Marion

Download or read book Classical Dynamics of Particles and Systems written by Jerry B. Marion. This book was released on 2013-10-22. Available in PDF, EPUB and Kindle. Book excerpt: Classical Dynamics of Particles and Systems presents a modern and reasonably complete account of the classical mechanics of particles, systems of particles, and rigid bodies for physics students at the advanced undergraduate level. The book aims to present a modern treatment of classical mechanical systems in such a way that the transition to the quantum theory of physics can be made with the least possible difficulty; to acquaint the student with new mathematical techniques and provide sufficient practice in solving problems; and to impart to the student some degree of sophistication in handling both the formalism of the theory and the operational technique of problem solving. Vector methods are developed in the first two chapters and are used throughout the book. Other chapters cover the fundamentals of Newtonian mechanics, the special theory of relativity, gravitational attraction and potentials, oscillatory motion, Lagrangian and Hamiltonian dynamics, central-force motion, two-particle collisions, and the wave equation.

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