The Quantum Recipe

2020 ◽  
pp. 27-55
Author(s):  
Jochen Autschbach
Keyword(s):  
Quantum Mechanics ◽  
Quantum Entanglement ◽  
Variation Principle ◽  
Nonrelativistic Quantum ◽  
Expectation Values ◽  
System Of Particles ◽  
Quantum Hamiltonian ◽  
Heisenberg Uncertainty ◽  
Quantum Operators ◽  
Set Up

Introduction of the postulates of quantum mechanics: Wavefunctions, operators, observables, commutating operators, expectation values, probabilities, Heisenberg uncertainty. The postulates are then used to set up a ‘quantum recipe’, i.e. a straightforward recipe by which to write down the (nonrelativistic) quantum Hamiltonian of a system of particles. This chapter also discusses the representation of quantum operators as matrices, in reference to a set of ‘basis’ functions, and the variation principle. The idea of a particle trajectory must be abandoned in quantum mechanics. Observable properties of a particle correspond to eigenvalues of the associated quantum operators. The chapter concludes with a brief discussion of the Schrodinger’s cat paradox, quantum entanglement, and other oddities.

scholarly journals Non-Stationary States in Physics and Biophysics

2020 ◽  
pp. 61-67
Author(s):  
Б. Г. Заславский ◽  
М. А. Филатов ◽  
В. В. Еськов ◽  
Е. А. Манина
Keyword(s):  
Quantum Mechanics ◽  
Quantum Entanglement ◽  
Uncertainty Principle ◽  
Stationary States ◽  
Unstable Systems ◽  
Heisenberg Uncertainty Principle ◽  
Human Habitat ◽  
Heisenberg Uncertainty ◽  
Self Organizing

Необходимость изучения неустойчивых систем подчеркивал I. R. Prigogine, но за последние 40 лет эта проблема не рассматривается в науке. Однако за последние 25 лет была доказана статистическая неустойчивость параметров движения в биомеханике в виде эффекта Еськова–Зинченко. Подобные неустойчивые системы имеются и в неживой природе на Земле в виде систем регуляции климата и метеопараметров среды обитания человека. Эти системы в 1948 г. W. Weaver обозначил как системы третьего типа, они обладают особой статистической неустойчивостью, характерной для самоорганизующихся систем. В работе представлены основные свойства таких систем третьего типа и некоторые инварианты для их описания. Существенно, что их моделирование основано на ряде принципов квантовой механики. В частности, принципе неопределенности Гейзенберга и квантовой запутанности. I. R. Prigogine emphasized the need to research unstable systems. However, for the last 40 years, this problem has not been studied well. Still, in the last 25 years, the statistical instability of biomechanical motion properties was proved as the Eskov–Zinchenko effect. Such unstable systems exist in the Earth’s inorganic nature, too, as the human habitat climate/weather regulation systems. In 1948 W. Weather called such systems “3rd kind systems”. They feature a special statistical instability peculiar to self-organizing systems. The study presents the key properties of such 3rd kind systems and some invariants that define these non-stationary systems. Significantly, the simulation is based on some quantum mechanics postulates. Particularly, these are the Heisenberg uncertainty principle, and the quantum entanglement principle.

scholarly journals IRROTATIONAL MOMENTUM FLUCTUATIONS CONDITIONING THE QUANTUM NATURE OF PHYSICAL PROCESSES

2006 ◽  
Vol 21 (26) ◽  
pp. 5299-5316
Author(s):  
STEPHAN I. TZENOV
Keyword(s):  
Quantum Mechanics ◽  
Statistical Mechanics ◽  
Correspondence Principle ◽  
Quantum Mechanical ◽  
Physical Processes ◽  
Expectation Values ◽  
Heisenberg Uncertainty Principle ◽  
Quantum Formalism ◽  
Classical Statistical Mechanics ◽  
Heisenberg Uncertainty

Starting from a simple classical framework and employing some stochastic concepts, the basic ingredients of the quantum formalism are recovered. It has been shown that the traditional axiomatic structure of quantum mechanics can be rebuilt, so that the quantum mechanical framework resembles to a large extent that of the classical statistical mechanics and hydrodynamics. The main assumption used here is the existence of a random irrotational component in the classical momentum. Various basic elements of the quantum formalism (calculation of expectation values, the Heisenberg uncertainty principle, the correspondence principle) are recovered by applying traditional techniques, borrowed from classical statistical mechanics.

scholarly journals On Certain Analogies Between the Laws of Quantum Mechanics and Rules of an English Auction

2012 ◽  
Vol 10 (2) ◽  
pp. 19-34
Author(s):  
Ewa Drabik
Keyword(s):  
Quantum Mechanics ◽  
Financial Markets ◽  
Financial Market ◽  
Second Law Of Thermodynamics ◽  
English Auction ◽  
Heisenberg Uncertainty Principle ◽  
Wave Particle Duality ◽  
System Of Particles ◽  
Auction Mechanisms ◽  
Heisenberg Uncertainty

On Certain Analogies Between the Laws of Quantum Mechanics and Rules of an English Auction It is a self-evident truth that nowadays a growing number of economic phenomena is described by means of physics methods. The most frequent theories derived from physics and applied to economy are: (1) the universal gravitation law and (2) the first as well as the second law of thermodynamics. The methods of static physics are applicable also to the theory of financial markets. In this case it is assumed that the financial market is composed of single participants interacting as a system of particles. Such approach is associated with a model of financial market otherwise known as a minority game. It is postulated that the process of securities and money allocation is performed on the basis of prices fluctuation, where - if a vast majority of investors tend to purchase goods or services - the sale constitutes a more profitable option, and vice versa. The players who end up on minority side win. At the end of the XX century the economy commenced to apply the laws of quantum mechanics. These laws proved to be useful, in particular when attempting to generalize game theory, which resulted in quantum games. The aim of the paper is to compare the rules and auction mechanisms with selected laws of quantum mechanics. This paper aims also to introduce the basic concepts of quantum mechanics to the process of economic phenomena modeling. Quantum mechanics is a theory describing a behaviour of microscopic objects and is grounded on the principle of wave-particle duality. It is assumed that quantum-scale objects at the same time exhibit both wave-like and particle-like properties. The key role in quantum mechanics is played by: (1) the Schrödinger equation describing the probability amplitude for the particle to be found at a given position and at a given time, as well as (2) the Heisenberg uncertainty principle stating that a certain pair of physical properties may not be simultaneously measured to arbitrarily high precision.

scholarly journals ABCD of ’t Hooft operators

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hirotaka Hayashi ◽  
Takuya Okuda ◽  
Yutaka Yoshida
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theories ◽  
Supersymmetric Quantum Mechanics ◽  
Type Ii ◽  
Expectation Values ◽  
String Theories

Abstract We compute by supersymmetric localization the expectation values of half-BPS ’t Hooft line operators in $$ \mathcal{N} $$ N = 2 U(N ), SO(N ) and USp(N ) gauge theories on S1 × ℝ3 with an Ω-deformation. We evaluate the non-perturbative contributions due to monopole screening by calculating the supersymmetric indices of the corresponding supersymmetric quantum mechanics, which we obtain by realizing the gauge theories and the ’t Hooft operators using branes and orientifolds in type II string theories.

scholarly journals An analysis on Quantum mechanical Stability of Regular Polygons on a Point Base Using Heisenberg Uncertainty Principle

2021 ◽  
Vol 9 (10) ◽  
pp. 74-79
Author(s):  
Anurag Chapagain
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Stability Problem ◽  
Classical Mechanics ◽  
Quantum Mechanical ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty ◽  
Degree Of Stability ◽  
The Stability ◽  
Heisenberg's Uncertainty Principle

Abstract: It is a well-known fact in physics that classical mechanics describes the macro-world, and quantum mechanics describes the atomic and sub-atomic world. However, principles of quantum mechanics, such as Heisenberg’s Uncertainty Principle, can create visible real-life effects. One of the most commonly known of those effects is the stability problem, whereby a one-dimensional point base object in a gravity environment cannot remain stable beyond a time frame. This paper expands the stability question from 1- dimensional rod to 2-dimensional highly symmetrical structures, such as an even-sided polygon. Using principles of classical mechanics, and Heisenberg’s uncertainty principle, a stability equation is derived. The stability problem is discussed both quantitatively as well as qualitatively. Using the graphical analysis of the result, the relation between stability time and the number of sides of polygon is determined. In an environment with gravity forces only existing, it is determined that stability increases with the number of sides of a polygon. Using the equation to find results for circles, it was found that a circle has the highest degree of stability. These results and the numerical calculation can be utilized for architectural purposes and high-precision experiments. The result is also helpful for minimizing the perception that quantum mechanical effects have no visible effects other than in the atomic, and subatomic world. Keywords: Quantum mechanics, Heisenberg Uncertainty principle, degree of stability, polygon, the highest degree of stability

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