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 Relativistic quantum mechanics

1932 ◽  
Vol 136 (829) ◽  
pp. 453-464 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Classical Theory ◽  
Correspondence Principle ◽  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Hamiltonian Function ◽  
Relativistic Quantum Mechanics ◽  
Classical Electrodynamics ◽  
Quantum Phenomena

The steady development of the quantum theory that has taken place during the present century was made possible only by continual reference to the Correspondence Principle of Bohr, according to which, classical theory can give valuable information about quantum phenomena in spite of the essential differences in the fundamental ideas of the two theories. A masterful advance was made by Heisenberg in 1925, who showed how equations of classical physics could be taken over in a formal way and made to apply to quantities of importance in quantum theory, thereby establishing the Correspondence Principle on a quantitative basis and laying the foundations of the new Quantum Mechanics. Heisenberg’s scheme was found to fit wonderfully well with the Hamiltonian theory of classical mechanics and enabled one to apply to quantum theory all the information that classical theory supplies, in so far as this information is consistent with the Hamiltonian form. Thus one was able to build up a satisfactory quantum mechanics for dealing with any dynamical system composed of interacting particles, provided the interaction could be expressed by means of an energy term to be added to the Hamiltonian function. This does not exhaust the sphere of usefulness of the classical theory. Classical electrodynamics, in its accurate (restricted) relativistic form, teaches us that the idea of an interaction energy between particles is only an approxi­mation and should be replaced by the idea of each particle emitting waves which travel outward with a finite velocity and influence the other particles in passing over them. We must find a way of taking over this new information into the quantum theory and must set up a relativistic quantum mechanics, before we can dispense with the Correspondence Principle.

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.

Quantization and Group Representations

1977 ◽  
Vol 29 (6) ◽  
pp. 1264-1276 ◽  
Author(s):  
R. Cressman
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Phase Space ◽  
Mechanical System ◽  
Correspondence Principle ◽  
Classical Mechanics ◽  
Quantum Mechanical ◽  
Group Representations ◽  
Additional Requirement ◽  
Adjoint Operators

A quantization of a fixed classical mechanical system is firstly an association between quantum mechanical observables (preferably self-adjoint operators on Hilbert space) and classical mechanical observables (i.e. real-valued functions on phase space). Secondly, a quantization should permit an interpretation of the correspondence principle that ‘classical mechanics is the limit of quantum mechanics as Planck's constant approaches zero'. With these two underlying precepts, Section 2 states the four basic requirements, I to IV, of a quantization along with an additional requirement V that characterizes the subclass of special quantizations.

scholarly journals IMPLICATIONS OF A QUANTUM MECHANICAL TREATMENT OF THE UNIVERSE

1998 ◽  
Vol 13 (05) ◽  
pp. 347-351 ◽  
Author(s):  
MURAT ÖZER
Keyword(s):  
Quantum Mechanics ◽  
Wave Packet ◽  
Early Universe ◽  
Mechanical Treatment ◽  
Correspondence Principle ◽  
Scale Factor ◽  
Quantum Mechanical ◽  
Quantum Mechanical Treatment ◽  
The Standard Model ◽  
The Universe

We attempt to treat the very early Universe according to quantum mechanics. Identifying the scale factor of the Universe with the width of the wave packet associated with it, we show that there cannot be an initial singularity and that the Universe expands. Invoking the correspondence principle, we obtain the scale factor of the Universe and demonstrate that the causality problem of the standard model is solved.

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 Analytical mathematical schemes: Circular rod grounded via transverse Poisson’s effect and extensive wave propagation on the surface of water

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 545-554
Author(s):  
Asghar Ali ◽  
Aly R. Seadawy ◽  
Dumitru Baleanu
Keyword(s):  
Wave Propagation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Longitudinal Wave ◽  
Symbolic Computation ◽  
Boussinesq Equation ◽  
Nonlinear Partial Differential Equations ◽  
Wave Model ◽  
Simple Equation ◽  
Partial Differential

AbstractThis article scrutinizes the efficacy of analytical mathematical schemes, improved simple equation and exp(-\text{Ψ}(\xi ))-expansion techniques for solving the well-known nonlinear partial differential equations. A longitudinal wave model is used for the description of the dispersion in the circular rod grounded via transverse Poisson’s effect; similarly, the Boussinesq equation is used for extensive wave propagation on the surface of water. Many other such types of equations are also solved with these techniques. Hence, our methods appear easier and faster via symbolic computation.

Hybrid Quantum Mechanics/Molecular Mechanics (QM/MM) Simulation: A Tool for Structure-based Drug Design and Discovery

2021 ◽  
Vol 21 ◽  
Author(s):  
Prajakta U. Kulkarni ◽  
Harshil Shah ◽  
Vivek K. Vyas
Keyword(s):  
Quantum Mechanics ◽  
Drug Design ◽  
Molecular Mechanics ◽  
Chemical Reactions ◽  
Classical Mechanics ◽  
Molecular Structures ◽  
Protein Crystal ◽  
Structure Based Drug Design ◽  
Structure And Property ◽  
Qsar Models

: Quantum mechanics (QM) is physics based theory which explains the physical properties of nature at the level of atoms and sub-atoms. Molecular mechanics (MM) construct molecular systems through the use of classical mechanics. So, hybrid quantum mechanics and molecular mechanics (QM/MM) when combined together can act as computer-based methods which can be used to calculate structure and property data of molecular structures. Hybrid QM/MM combines the strengths of QM with accuracy and MM with speed. QM/MM simulation can also be applied for the study of chemical process in solutions as well as in the proteins, and has a great scope in structure-based drug design (CADD) and discovery. Hybrid QM/MM also applied to HTS, to derive QSAR models and due to availability of many protein crystal structures; it has a great role in computational chemistry, especially in structure- and fragment-based drug design. Fused QM/MM simulations have been developed as a widespread method to explore chemical reactions in condensed phases. In QM/MM simulations, the quantum chemistry theory is used to treat the space in which the chemical reactions occur; however the rest is defined through molecular mechanics force field (MMFF). In this review, we have extensively reviewed recent literature pertaining to the use and applications of hybrid QM/MM simulations for ligand and structure-based computational methods for the design and discovery of therapeutic agents.

Subsequent and Subsidiary? Rethinking the Role of Applications in Establishing Quantum Mechanics

2015 ◽  
Vol 45 (5) ◽  
pp. 641-702 ◽  
Author(s):  
Jeremiah James ◽  
Christian Joas
Keyword(s):  
Molecular Structure ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Classical Mechanics ◽  
Theory Construction ◽  
Science Pedagogy ◽  
Old Quantum Theory ◽  
The Common ◽  
Complete Quantum

As part of an attempt to establish a new understanding of the earliest applications of quantum mechanics and their importance to the overall development of quantum theory, this paper reexamines the role of research on molecular structure in the transition from the so-called old quantum theory to quantum mechanics and in the two years immediately following this shift (1926–1928). We argue on two bases against the common tendency to marginalize the contribution of these researches. First, because these applications addressed issues of longstanding interest to physicists, which they hoped, if not expected, a complete quantum theory to address, and for which they had already developed methods under the old quantum theory that would remain valid under the new mechanics. Second, because generating these applications was one of, if not the, principal means by which physicists clarified the unity, generality, and physical meaning of quantum mechanics, thereby reworking the theory into its now commonly recognized form, as well as developing an understanding of the kinds of predictions it generated and the ways in which these differed from those of the earlier classical mechanics. More broadly, we hope with this article to provide a new viewpoint on the importance of problem solving to scientific research and theory construction, one that might complement recent work on its role in science pedagogy.

Sign in / Sign up

Export Citation Format

Share Document