scholarly journals Classical and Quantum Physics in Selected Economic Models

2011 ◽  
Vol 3 (1) ◽  
pp. 7-20 ◽  
Author(s):  
Ewa Drabik
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Financial Markets ◽  
Uncertainty Principle ◽  
Schrodinger Equation ◽  
Quantum Physics ◽  
Economic Models ◽  
Heisenberg Uncertainty Principle ◽  
Wave Particle Duality ◽  
Heisenberg Uncertainty

Classical and Quantum Physics in Selected Economic ModelsA growing number of economic phenomena are nowadays described with methods known in physics. The most frequently applied physical theories by economists are: (1) the universal gravitation law and (2) the first and second law of thermodynamics. Physical principles can also be applied to the theory of financial markets. Financial markets are composed of individual participants who may be seen to interact as particles in a physical system. This approach proposes a financial market model known as a minority game model in which securities and money are allocated on the basis of price fluctuations, and where selling is best option when the vast majority of investors tend to purchase goods or services, and vice versa. The players who end up being on the minority side win.The above applications of physical methods in economics are deeply rooted in classical physics. However, this paper aims to introduce the basic concepts of quantum mechanics to the process of economic phenomena modelling. Quantum mechanics is a theory describing the 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 in a given position and at a given time, and as (2) the Heisenberg uncertainty principle stating that certain pairs of physical properties cannot be economic applications of the Schrödinger equation as well as the Heisenberg uncertainty principle. We also try to describe the English auction by means the quantum mechanics methods.

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 QUANTUM CRYPTOGRAPHY: A NEW APPROACH TO INFORMATION SECURITY

2011 ◽  
pp. 11-13
Author(s):  
Rishi Dutt Sharma
Keyword(s):  
Quantum Mechanics ◽  
Quantum Cryptography ◽  
Uncertainty Principle ◽  
Quantum Physics ◽  
Research Paper ◽  
Photon Polarization ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty ◽  
Secure Network ◽  
Future Direction

Quantum cryptography is an emerging technology in which two parties can secure network Communications by applying the phenomena of quantum physics. The security of these transmissions is based on the inviolability of the laws of quantum mechanics. Quantum cryptography was born in the early seventies when Steven wiesner wrote “conjugate coding”. The quantum cryptography relies on two important elements of quantum mechanics-the Heisenberg uncertainty principle and the principle of photon polarization. The Heisenberg uncertainty principle states that, it is not possible to measure the quantum state of any system without distributing that system. The principle of photon polarization states that, an eavesdropper cannot copy unknownqubits i.e. unknown quantum states, due to no-cloning Theorem which was first presented by wootters andzurek in 1982.this research paper concentrates on the theory of quantum cryptography, and how this technology contributes to the network security. This research paper summarizes the current state of Quantum cryptography, and the real world application implementation of this technology and finally the future direction in which quantum cryptography is forwards

scholarly journals General Quantum Theory: I ---- Deducing Quantum Physics and Solving Two Origin Crisises of Wave-Particle Duality and the First Quantization

2021 ◽  
Author(s):  
C. Huang ◽  
Yong-Chang Huang ◽  
Jia-Min Song
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Statistical Mechanics ◽  
Schrodinger Equation ◽  
Quantum Physics ◽  
Time Derivative ◽  
Square Root ◽  
Classical Statistical Mechanics ◽  
Wave Particle Duality ◽  
Solid Bases

Density distribution function of classical statistical mechanics is generally generalized as a product of a general complex function and its complex Hermitian conjugate function, and the average of classical statistical mechanics is generalized as the average of the quantum mechanics. Furthermore, this paper derives three ones of the five axiom presumptions of quantum mechanics, e.g., deduces Schrȍdinger equation by two general ways, makes the three axiom presumptions into three theorems of quantum mechanics, not only solves the crisis to hard understand, but also gets new theories and new discoveries, e.g., this paper solves the crisis of the origin of the wave-particle duality, derives operators, eigenvalues and eigenstates, deduces commutation relations for coordinate and momentum as well as the time and energy, and discovers quantum mechanics is just a generalization ( mechanics ) theory of the complex square root of ( real density function of ) classical statistical mechanics. Quantum mechanics being just a generalization theory of the complex square root of classical statistical mechanics is both new physics and revolutionary discovery, which are affecting people’s deep philosophical thinking for modern physics development, solve all the crisises of quantum mechanics, quantum information and so on, and make quantum mechanics have scientific solid bases being checked and both no basic axiom presumption and no all the quantum strange incomprehensible properties, because classical statistical mechanics and the complex square root of classical statistical mechanics have the scientific solid bases being checked. In addition, this paper discovers the reason no taking the time derivative of space coordinates in Schrȍdinger equation. Therefore, this paper gives solution to the crisis of the first quantization origin, and mainly deduces quantum physics no all the quantum current strange incomprehensible properties.

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

scholarly journals A CLASS OF GUP SOLUTIONS IN DEFORMED QUANTUM MECHANICS

2010 ◽  
Vol 19 (12) ◽  
pp. 2003-2009 ◽  
Author(s):  
POURIA PEDRAM
Keyword(s):  
Black Hole ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Loop Quantum Gravity ◽  
Black Hole Physics ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Uncertainty Principle ◽  
Deformed Algebra ◽  
Heisenberg Uncertainty

Various candidates of quantum gravity such as string theory, loop quantum gravity and black hole physics all predict the existence of a minimum observable length which modifies the Heisenberg uncertainty principle to the so-called generalized uncertainty principle (GUP). This approach results from the modification of the commutation relations and changes all Hamiltonians in quantum mechanics. In this paper, we present a class of physically acceptable solutions for a general commutation relation without directly solving the corresponding generalized Schrödinger equations. These solutions satisfy the boundary conditions and exhibit the effect of the deformed algebra on the energy spectrum. We show that this procedure prevents us from doing equivalent but lengthy calculations.

WIGNER FUNCTION APPROACH TO OSCILLATING SOLUTIONS OF THE 1D-QUINTIC NONLINEAR SCHRÖDINGER EQUATION

2013 ◽  
Vol 22 (02) ◽  
pp. 1350013 ◽  
Author(s):  
ALEX MAHALOV ◽  
SERGEI K. SUSLOV
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Heisenberg Uncertainty Principle ◽  
Nonlinear Schrödinger ◽  
Oscillating Solutions ◽  
Heisenberg Uncertainty ◽  
Quintic Nonlinear Schrödinger Equation ◽  
Quasiprobability Distribution

In this paper, we study oscillating solutions of the 1D-quintic nonlinear Schrödinger equation with the help of Wigner's quasiprobability distribution in quantum phase space. An "absolute squeezing property", namely a periodic in time total localization of wave packets at some finite spatial points without violation of the Heisenberg uncertainty principle, is analyzed in this nonlinear model.

scholarly journals If quantum mechanics is the solution, what should the problem be?

2020 ◽  
Author(s):  
Vasil Penchev
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Real Problem ◽  
Many Worlds ◽  
Interpretations Of Quantum Mechanics ◽  
Wave Particle Duality ◽  
History Of ◽  
The Common ◽  
Universal Law

The paper addresses the problem, which quantum mechanics resolves in fact. Its viewpoint suggests that the crucial link of time and its course is omitted in understanding the problem. The common interpretation underlain by the history of quantum mechanics sees discreteness only on the Plank scale, which is transformed into continuity and even smoothness on the macroscopic scale. That approach is fraught with a series of seeming paradoxes. It suggests that the present mathematical formalism of quantum mechanics is only partly relevant to its problem, which is ostensibly known. The paper accepts just the opposite: The mathematical solution is absolute relevant and serves as an axiomatic base, from which the real and yet hidden problem is deduced. Wave-particle duality, Hilbert space, both probabilistic and many-worlds interpretations of quantum mechanics, quantum information, and the Schrödinger equation are included in that base. The Schrödinger equation is understood as a generalization of the law of energy conservation to past, present, and future moments of time. The deduced real problem of quantum mechanics is: “What is the universal law describing the course of time in any physical change therefore including any mechanical motion?”

scholarly journals The Heisenberg Uncertainty Principle as an Endogenous Equilibrium Property of Stochastic Optimal Control Systems in Quantum Mechanics

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1533 ◽  
Author(s):  
Jussi Lindgren ◽  
Jukka Liukkonen
Keyword(s):  
Optimal Control ◽  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Stochastic Optimal Control ◽  
Stochastic Approach ◽  
Heisenberg Uncertainty Principle ◽  
Control Approach ◽  
Heisenberg Uncertainty ◽  
Original Interpretation ◽  
Optimal Control Approach

We provide a natural derivation and interpretation for the uncertainty principle in quantum mechanics from the stochastic optimal control approach. We show that, in particular, the stochastic approach to quantum mechanics allows one to understand the uncertainty principle through the “thermodynamic equilibrium”. A stochastic process with a gradient structure is key in terms of understanding the uncertainty principle and such a framework comes naturally from the stochastic optimal control approach to quantum mechanics. The symmetry of the system is manifested in certain non-vanishing and invariant covariances between the four-position and the four-momentum. In terms of interpretation, the results allow one to understand the uncertainty principle through the lens of scientific realism, in accordance with empirical evidence, contesting the original interpretation given by Heisenberg.

Sign in / Sign up

Export Citation Format

Share Document