Exploring Classical Mechanics

2020 ◽  
Author(s):  
G. L. Kotkin ◽  
V. G. Serbo
Keyword(s):  
Quantum Mechanics ◽  
Statistical Mechanics ◽  
Classical Mechanics ◽  
Theoretical Physics ◽  
English Edition ◽  
Mechanical Part ◽  
Russian Edition ◽  
The Given

This book was written by the working physicists for students and teachers of physics faculties of universities. Its contents correspond roughly to the corresponding course in the textbooks Mechanics by L. D. Landau and E. M. Lifshitz (1976) and Classical Mechanics by H. Goldstein, Ch. Poole, and J. Safko (2000). As a rule, the given solution of a problem is not finished with obtaining the required formulae. It is necessary to analyse the results, and this is of great interest and by no means a mechanical part of the solution. The authors consider classical mechanics as the first chapter of theoretical physics; the methods and ideas developed in this chapter are literally important for all other sections of theoretical physics. Thus, the authors have indicated wherever this does not require additional amplification, the analogy or points of contact with the problems in quantum mechanics, electrodynamics, or statistical mechanics. The first English edition of this book was published by Pergamon Press in 1971 with the invaluable help by the translation editor D. ter Haar. This second English publication is based on the fourth Russian edition of 2010 as well as the problems added in the publications in Spanish and French. As a result, this book contains 357 problems instead of the 289 problems that appeared in the first English edition.

A short course on quantum mechanics and methods of quantization

2015 ◽  
Vol 12 (08) ◽  
pp. 1560008 ◽  
Author(s):  
Elisa Ercolessi
Keyword(s):  
Quantum Mechanics ◽  
Hilbert Spaces ◽  
International Workshop ◽  
Classical Mechanics ◽  
Theoretical Physics ◽  
Feynman Path Integral ◽  
Introductory Courses ◽  
Feynman Path ◽  
Geometric Structures ◽  
Short Course

These notes collect the lectures given by the author to the "XXIII International Workshop on Geometry and Physics" held in Granada (Spain) in September 2014. The first part of this paper aims at introducing a mathematical oriented reader to the realm of Quantum Mechanics (QM) and then to present the geometric structures that underline the mathematical formalism of QM which, contrary to what is usually done in Classical Mechanics (CM), are usually not taught in introductory courses. The mathematics related to Hilbert spaces and Differential Geometry are assumed to be known by the reader. In the second part, we concentrate on some quantization procedures, that are founded on the geometric structures of QM — as we have described them in the first part — and represent the ones that are more operatively used in modern theoretical physics. We will discuss first the so-called Coherent State Approach which, mainly complemented by "Feynman Path Integral Technique", is the method which is most widely used in quantum field theory. Finally, we will describe the "Weyl Quantization Approach" which is at the origin of modern tomographic techniques, originally used in optics and now in quantum information theory.

scholarly journals GENERALIZATION OF CLASSICAL STATISTICAL MECHANICS TO QUANTUM MECHANICS AND STABLE PROPERTY OF CONDENSED MATTER

2004 ◽  
Vol 18 (26n27) ◽  
pp. 1367-1377 ◽  
Author(s):  
Y. C. HUANG ◽  
F. C. MA ◽  
N. ZHANG
Keyword(s):  
Quantum Mechanics ◽  
Statistical Mechanics ◽  
Uncertainty Principle ◽  
Classical Limit ◽  
Condensed Matter ◽  
Superposition Principle ◽  
Classical Mechanics ◽  
Eigenvalue Equation ◽  
Quantum Uncertainty ◽  
Classical Statistical Mechanics

Classical statistical average values are generally generalized to average values of quantum mechanics. It is discovered that quantum mechanics is a direct generalization of classical statistical mechanics, and we generally deduce both a new general continuous eigenvalue equation and a general discrete eigenvalue equation in quantum mechanics, and discover that a eigenvalue of quantum mechanics is just an extreme value of an operator in possibility distribution, the eigenvalue f is just classical observable quantity. A general classical statistical uncertain relation is further given, and the general classical statistical uncertain relation is generally generalized to the quantum uncertainty principle; the two lost conditions in classical uncertain relation and quantum uncertainty principle, respectively, are found. We generally expound the relations among the uncertainty principle, singularity and condensed matter stability, discover that the quantum uncertainty principle prevents the appearance of singularity of the electromagnetic potential between nucleus and electrons, and give the failure conditions of the quantum uncertainty principle. Finally, we discover that the classical limit of quantum mechanics is classical statistical mechanics, the classical statistical mechanics may further be degenerated to classical mechanics and we discover that merely stating that the classical limit of quantum mechanics is classical mechanics is a mistake. As application examples, we deduce both the Schrödinger equation and the state superposition principle, and deduce that there exists a decoherent factor from a general mathematical representation of the state superposition principle; the consistent difficulty between statistical interpretation of quantum mechanics and determinant property of classical mechanics is overcome.

scholarly journals CLASSICAL LIMIT OF THE TRAJECTORY REPRESENTATION OF QUANTUM MECHANICS, LOSS OF INFORMATION AND RESIDUAL INDETERMINACY

2000 ◽  
Vol 15 (09) ◽  
pp. 1363-1378 ◽  
Author(s):  
EDWARD R. FLOYD
Keyword(s):  
Quantum Mechanics ◽  
Statistical Mechanics ◽  
Classical Limit ◽  
Correspondence Principle ◽  
Classical Mechanics ◽  
Information Loss ◽  
Equivalence Classes ◽  
Trajectory Representation ◽  
Heisenberg Uncertainty ◽  
The Relationship

The trajectory representation in the classical limit (ℏ→0) manifests a residual indeterminacy. We show that the trajectory representation in the classical limit goes to neither classical mechanics (Planck's correspondence principle) nor statistical mechanics. This residual indeterminacy is contrasted to Heisenberg uncertainty. We discuss the relationship between residual indeterminacy and 't Hooft's information loss and equivalence classes.

scholarly journals Beyond Boltzmann–Gibbs–Shannon in Physics and Elsewhere

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 696 ◽  
Author(s):  
Constantino Tsallis
Keyword(s):  
Statistical Mechanics ◽  
Long Range ◽  
Communication Theory ◽  
Nonlinear Dynamical Systems ◽  
Initial Conditions ◽  
Classical Mechanics ◽  
Theoretical Physics ◽  
Von Neumann Entropy ◽  
Scale Free ◽  
Wide Range

The pillars of contemporary theoretical physics are classical mechanics, Maxwell electromagnetism, relativity, quantum mechanics, and Boltzmann–Gibbs (BG) statistical mechanics –including its connection with thermodynamics. The BG theory describes amazingly well the thermal equilibrium of a plethora of so-called simple systems. However, BG statistical mechanics and its basic additive entropy S B G started, in recent decades, to exhibit failures or inadequacies in an increasing number of complex systems. The emergence of such intriguing features became apparent in quantum systems as well, such as black holes and other area-law-like scenarios for the von Neumann entropy. In a different arena, the efficiency of the Shannon entropy—as the BG functional is currently called in engineering and communication theory—started to be perceived as not necessarily optimal in the processing of images (e.g., medical ones) and time series (e.g., economic ones). Such is the case in the presence of generic long-range space correlations, long memory, sub-exponential sensitivity to the initial conditions (hence vanishing largest Lyapunov exponents), and similar features. Finally, we witnessed, during the last two decades, an explosion of asymptotically scale-free complex networks. This wide range of important systems eventually gave support, since 1988, to the generalization of the BG theory. Nonadditive entropies generalizing the BG one and their consequences have been introduced and intensively studied worldwide. The present review focuses on these concepts and their predictions, verifications, and applications in physics and elsewhere. Some selected examples (in quantum information, high- and low-energy physics, low-dimensional nonlinear dynamical systems, earthquakes, turbulence, long-range interacting systems, and scale-free networks) illustrate successful applications. The grounding thermodynamical framework is briefly described as well.

Sound as a transverse wave

2017 ◽  
Vol 13 (1) ◽  
pp. 4522-4534
Author(s):  
Armando Tomás Canero
Keyword(s):  
Quantum Mechanics ◽  
Gravitational Waves ◽  
Longitudinal Wave ◽  
Transverse Wave ◽  
Sound Propagation ◽  
Correspondence Principle ◽  
Classical Mechanics ◽  
Wave Model ◽  
Scientific Experiments

This paper presents sound propagation based on a transverse wave model which does not collide with the interpretation of physical events based on the longitudinal wave model, but responds to the correspondence principle and allows interpreting a significant number of scientific experiments that do not follow the longitudinal wave model. Among the problems that are solved are: the interpretation of the location of nodes and antinodes in a Kundt tube of classical mechanics, the traslation of phonons in the vacuum interparticle of quantum mechanics and gravitational waves in relativistic mechanics.

scholarly journals From the Universe to Subsystems: Why Quantum Mechanics Appears More Stochastic than Classical Mechanics

2016 ◽  
Vol 15 (03) ◽  
pp. 1640002 ◽  
Author(s):  
Andrea Oldofredi ◽  
Dustin Lazarovici ◽  
Dirk-André Deckert ◽  
Michael Esfeld
Keyword(s):  
Quantum Mechanics ◽  
Classical Mechanics ◽  
Bohmian Quantum Mechanics ◽  
The Universe

By means of the examples of classical and Bohmian quantum mechanics, we illustrate the well-known ideas of Boltzmann as to how one gets from laws defined for the universe as a whole the dynamical relations describing the evolution of subsystems. We explain how probabilities enter into this process, what quantum and classical probabilities have in common and where exactly their difference lies.

scholarly journals Introduction to Theoretical Physics: Classical Mechanics and Electrodynamics

1964 ◽  
Vol 32 (7) ◽  
pp. 577-577
Author(s):  
Roald K. Wangsness ◽  
Peter B. Kahn
Keyword(s):  
Classical Mechanics ◽  
Theoretical Physics
Sign in / Sign up

Export Citation Format

Share Document