Multiple Quantization

1953 ◽  
Vol 5 ◽  
pp. 26-36
Author(s):  
A. E. Scheidegger
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Physical Science ◽  
Commutation Relations ◽  
Vast Amount ◽  
Physical Evidence

The efforts of most theoretical physicists of this century have been directed towards that branch of the physical science which is commonly called “Quantum Theory.” Physically, Quantum Theory was postulated because of a vast amount of physical evidence which led to the postulates of states, observables, superposition, and commutation relations. From these four postulates, all quantum mechanics follows.

scholarly journals Previously Unknown Physical Formulas which Hold in a Hydrogen Atom and are Derived without Using Quantum Mechanics

2017 ◽  
Vol 9 (4) ◽  
pp. 7
Author(s):  
Koshun Suto
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Hydrogen Atom ◽  
Physical Science ◽  
Classical Quantum ◽  
Physical Quantities

It is thought that quantum mechanics is the physical science describing the behavior of the electron in the micro world, e.g., inside a hydrogen atom. However, the author has previously derived the energy-momentum relationship which holds inside a hydrogen atom. This paper uses that relationship to investigate the relationships between physical quantities which hold in a hydrogen atom. In this paper, formulas are derived which hold in the micro world and make more accurate predictions than the classical quantum theory. This paper concludes that quantum mechanics is not the only theory enabling investigation of the micro world.

scholarly journals q-OSCILLATORS, NON-KÄHLER MANIFOLDS AND CONSTRAINED DYNAMICS

1995 ◽  
Vol 10 (12) ◽  
pp. 941-948 ◽  
Author(s):  
SERGEI V. SHABANOV
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Constrained Dynamics ◽  
Commutation Relations ◽  
Ordinary Quantum

It is shown that q-deformed quantum mechanics (systems with q-deformed Heisenberg commutation relations) can be interpreted as an ordinary quantum mechanics on Kähler manifolds, or as a quantum theory with second- (or first-) class constraints.

scholarly journals Examples of Non-Constructive Proofs in Quantum Theory

2015 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Arkady Bolotin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Infinite Number ◽  
Physical Science ◽  
Physical Theory ◽  
Quantum States ◽  
Standard Quantum ◽  
Macroscopic Quantum ◽  
Quantum Formalism ◽  
Constructive Proofs

<p class="1Body">Unlike mathematics, in which the notion of truth might be abstract, in physics, the emphasis must be placed on algorithmic procedures for obtaining numerical results subject to the experimental verifiability. For, a physical science is exactly that: algorithmic procedures (built on a certain mathematical formalism) for obtaining verifiable conclusions from a set of basic hypotheses. By admitting non-constructivist statements, a physical theory loses its concrete applicability and thus verifiability of its predictions. Accordingly, the requirement of constructivism must be indispensable to any physical theory. Nevertheless, in at least some physical theories, and especially in quantum mechanics, one can find examples of non-constructive statements. The present paper demonstrates a couple of such examples dealing with macroscopic quantum states (i.e., with the applicability of the standard quantum formalism to macroscopic systems). As it is shown, in these examples the proofs of the existence of macroscopic quantum states are based on logical principles allowing one to decide the truth of predicates over an infinite number of things.</p>

Quantum Computing Memoir: Quantum Mechanics, Architectural Developments and its Future

2021 ◽  
Vol 9 (8) ◽  
pp. 2198-2200
Author(s):  
Abhay Patil
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computing ◽  
Quantum Theory ◽  
Computer Science ◽  
Physical Science ◽  
Quantum Computer ◽  
Energy Utilization ◽  
Quantum Computers ◽  
Edge Method ◽  
Limited Scope

Abstract: Quantum computing is a cutting edge method of computing that depends on the study of quantum mechanics and its staggering marvels. It is an excellent blend of physical science, arithmetic, computer science and data hypothesis. It gives high computational force, less energy utilization and remarkable speed over old-style computers by controlling the conduct of little actual articles for example minuscule particles like iotas, electrons, photons, and so forth Here, we present a prologue to the crucial ideas and a few thoughts of quantum computing. To comprehend the true abilities and difficulties of a pragmatic quantum computer that can be dispatched financially, the paper covers the engineering, equipment, programming, plan, types and calculations that are explicitly needed by quantum computers. It reveals the ability of quantum computers that can affect our lives in different perspectives like network safety, traffic enhancement, medications, man-made reasoning and some more. Limited scope quantum computers are being grown as of late. This improvement is going towards an incredible future because of their high possible abilities and headways in continuous exploration. Prior to zeroing in on the meanings of a broadly useful quantum computer and investigating the force of the new emerging innovation, it is smarter to survey the beginning, possibilities, and restrictions of the current conventional computing. This data helps us in understanding the potential difficulties in creating outlandish and serious innovation. It will likewise give us an understanding of the continuous advancement in this field. Keywords: Realtime Systems, Programming Processors, Quantum Theory, Quantum Computing

Quantum Becoming?

2017 ◽  
Author(s):  
Craig Callender
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Time ◽  
Quantum Non Locality ◽  
Time Quantum ◽  
Temporal Becoming ◽  
Non Locality ◽  
Quantum Wavefunction

Two of quantum mechanics’ more famed and spooky features have been invoked in defending the idea that quantum time is congenial to manifest time. Quantum non-locality is said by some to make a preferred foliation of spacetime necessary, and the collapse of the quantum wavefunction is held to vindicate temporal becoming. Although many philosophers and physicists seek relief from relativity’s assault on time in quantum theory, assistance is not so easily found.

Surfing the Quantum World

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Musical Instrument ◽  
Popular Science ◽  
Quantum Spin ◽  
Exclusion Principle ◽  
Maximum Height ◽  
Core Concepts ◽  
The Many ◽  
The One

Surfing the Quantum World bridges the gap between in-depth textbooks and typical popular science books on quantum ideas and phenomena. Among its significant features is the description of a host of mind-bending phenomena, such as a quantum object being in two places at once or a certain minus sign being the most consequential in the universe. Much of its first part is historical, starting with the ancient Greeks and their concepts of light, and ending with the creation of quantum mechanics. The second part begins by applying quantum mechanics and its probability nature to a pedagogical system, the one-dimensional box, an analog of which is a musical-instrument string. This is followed by a gentle introduction to the fundamental principles of quantum theory, whose core concepts and symbolic representations are the foundation for most of the subsequent chapters. For instance, it is shown how quantum theory explains the properties of the hydrogen atom and, via quantum spin and Pauli’s Exclusion Principle, how it accounts for the structure of the periodic table. White dwarf and neutron stars are seen to be gigantic quantum objects, while the maximum height of mountains is shown to have a quantum basis. Among the many other topics considered are a variety of interference phenomena, those that display the wave properties of particles like electrons and photons, and even of large molecules. The book concludes with a wide-ranging discussion of interpretational and philosophic issues, introduced in Chapters 14 by entanglement and 15 by Schrödinger’s cat.

Quantum Theory

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Principle ◽  
Quantum Spin ◽  
Quantum States ◽  
Wave Functions ◽  
Symbolic Representations ◽  
Quantum Numbers ◽  
The Subject ◽  
Heisenberg's Uncertainty Principle

The subject of Chapter 8 is the fundamental principles of quantum theory, the abstract extension of quantum mechanics. Two of the entities explored are kets and operators, with kets being representations of quantum states as well as a source of wave functions. The quantum box and quantum spin kets are specified, as are the quantum numbers that identify them. Operators are introduced and defined in part as the symbolic representations of observable quantities such as position, momentum and quantum spin. Eigenvalues and eigenkets are defined and discussed, with the former identified as the possible outcomes of a measurement. Bras, the counterpart to kets, are introduced as the means of forming probability amplitudes from kets. Products of operators are examined, as is their role underpinning Heisenberg’s Uncertainty Principle. A variety of symbol manipulations are presented. How measurements are believed to collapse linear superpositions to one term of the sum is explored.

Constructing Quantum Mechanics

2019 ◽  
Author(s):  
Anthony Duncan ◽  
Michel Janssen
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Stark Effect ◽  
Zeeman Effect ◽  
Black Body ◽  
Black Body Radiation ◽  
Wave Mechanics ◽  
Specific Heats ◽  
Old Quantum Theory ◽  
Upper Level

This is the first of two volumes on the genesis of quantum mechanics. It covers the key developments in the period 1900–1923 that provided the scaffold on which the arch of modern quantum mechanics was built in the period 1923–1927 (covered in the second volume). After tracing the early contributions by Planck, Einstein, and Bohr to the theories of black‐body radiation, specific heats, and spectroscopy, all showing the need for drastic changes to the physics of their day, the book tackles the efforts by Sommerfeld and others to provide a new theory, now known as the old quantum theory. After some striking initial successes (explaining the fine structure of hydrogen, X‐ray spectra, and the Stark effect), the old quantum theory ran into serious difficulties (failing to provide consistent models for helium and the Zeeman effect) and eventually gave way to matrix and wave mechanics. Constructing Quantum Mechanics is based on the best and latest scholarship in the field, to which the authors have made significant contributions themselves. It breaks new ground, especially in its treatment of the work of Sommerfeld and his associates, but also offers new perspectives on classic papers by Planck, Einstein, and Bohr. Throughout the book, the authors provide detailed reconstructions (at the level of an upper‐level undergraduate physics course) of the cental arguments and derivations of the physicists involved. All in all, Constructing Quantum Mechanics promises to take the place of older books as the standard source on the genesis of quantum mechanics.

scholarly journals Experimental test of the Greenberger–Horne–Zeilinger-type paradoxes in and beyond graph states

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Zheng-Hao Liu ◽  
Jie Zhou ◽  
Hui-Xian Meng ◽  
Mu Yang ◽  
Qiang Li ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Success Probability ◽  
Quantum Foundations ◽  
Mixed States ◽  
Graph States ◽  
Hardy Type ◽  
Realistic Description ◽  
Entanglement Detection ◽  
Quantum Paradoxes

AbstractThe Greenberger–Horne–Zeilinger (GHZ) paradox is an exquisite no-go theorem that shows the sharp contradiction between classical theory and quantum mechanics by ruling out any local realistic description of quantum theory. The investigation of GHZ-type paradoxes has been carried out in a variety of systems and led to fruitful discoveries. However, its range of applicability still remains unknown and a unified construction is yet to be discovered. In this work, we present a unified construction of GHZ-type paradoxes for graph states, and show that the existence of GHZ-type paradox is not limited to graph states. The results have important applications in quantum state verification for graph states, entanglement detection, and construction of GHZ-type steering paradox for mixed states. We perform a photonic experiment to test the GHZ-type paradoxes via measuring the success probability of their corresponding perfect Hardy-type paradoxes, and demonstrate the proposed applications. Our work deepens the comprehension of quantum paradoxes in quantum foundations, and may have applications in a broad spectrum of quantum information tasks.

scholarly journals A relativistic basis of the quantum theory.—II

1934 ◽  
Vol 145 (855) ◽  
pp. 645-656 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Wave Equation ◽  
Quantum Theory ◽  
General Expression ◽  
Matrix Equation ◽  
Covariant Derivative ◽  
Riemannian Geometry ◽  
Order Equation ◽  
Second Order ◽  
Space Curvature

The paper is a continuation of the last paper communicated to these 'Proceedings.' In that paper, which we shall refer to as the first paper, a more general expression for space curvature was obtained than that which occurs in Riemannian geometry, by a modification of the Riemannian covariant derivative and by the use of a fifth co-ordinate. By means of a particular substitution (∆ μσ σ = 1/ψ ∂ψ/∂x μ ) it was shown that this curvature takes the form of the second order equation of quantum mechanics. It is not a matrix equation, however but one which has the character of the wave equation as it occurred in the earlier form of the quantum theory. But it contains additional terms, all of which can be readily accounted for in physics, expect on which suggested an identification with energy of the spin.

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