Quantum equations from Brownian motion

2011 ◽  
Vol 89 (2) ◽  
pp. 185-191 ◽  
Author(s):  
B. S. Rajput
Keyword(s):  
Uncertainty Principle ◽  
Free Particle ◽  
Continuous Limit ◽  
Order Effects ◽  
Heisenberg Uncertainty Principle ◽  
Classical Counterpart ◽  
Quantum Equation ◽  
Heisenberg Uncertainty ◽  
Lattice Random Walks ◽  
Quantum Equations

The Schrödinger free particle equation in 1+1 dimension describes second-order effects in ensembles of lattice random walks, in addition to its role in quantum mechanics, and its solutions represent the continuous limit of a property of ensembles of Brownian particles. In the present paper, the classical Schrödinger and Dirac equations have been derived from the Brownian motions of a particle, and it has been shown that the classical Schrödinger equation can be transformed into the usual Schrödinger quantum equation on applying the Heisenberg uncertainty principle between position and momentum, while the Dirac quantum equation follows from its classical counterpart on applying the Heisenberg uncertainty principle between energy and time, without applying any analytical continuation.

scholarly journals Prediction for the cosmological constant and constraints on SUSY GUTs in resummed quantum gravity

2018 ◽  
Vol 33 (29) ◽  
pp. 1830028
Author(s):  
B. F. L. Ward
Keyword(s):  
General Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Uncertainty Principle ◽  
Planck Scale ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty

Working in the context of the Planck scale cosmology formulation of Bonanno and Reuter, we use our resummed quantum gravity approach to Einstein’s general theory of relativity to estimate the value of the cosmological constant as [Formula: see text]. We show that SUSY GUT models are constrained by the closeness of this estimate to experiment. We also address various consistency checks on the calculation. In particular, we use the Heisenberg uncertainty principle to remove a large part of the remaining uncertainty in our estimate of [Formula: see text].

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

Mysteries of Unsustainable Public Finance and of Low Economic Growth

2020 ◽  
pp. 175-200
Author(s):  
Olga Ivanovna Pilipenko ◽  
Andrey Igorevich Pilipenko
Keyword(s):  
Public Finance ◽  
Economic Growth ◽  
Income Distribution ◽  
Uncertainty Principle ◽  
Economic Efficiency ◽  
The State ◽  
Heisenberg Uncertainty Principle ◽  
Economic Agents ◽  
Heisenberg Uncertainty ◽  
Low Efficiency

The authors structure the main functions of the state in the economic system as the “famous triad” of R. Musgrave. They are connected with allocating resources, redistributing income (equality in income distribution), and stabilizing economy (economic efficiency). The aim is to find the causes of their low efficient implementation by the state. This is manifested in the fact that society itself does not have the ability to adequately control the current activities of the state created and put over it in order to protect its interests; in the contradictory essence of the state itself, which is the regulator, which forms the rules of behavior of economic agents and at the same time acts as the economic agent participating in market transactions. To model the options for the effective resolution of the problems of the “magic triangle,” the authors formulated the Musgrave uncertainty principle by analogy with the Heisenberg uncertainty principle in physics. This makes it possible to assess the budget expenditures of the state in order to get out of its low efficiency trap.

PROTON LIFETIME AND SMOLUCHOWSKI EQUATION

1995 ◽  
Vol 10 (11) ◽  
pp. 911-915
Author(s):  
P.R. SILVA
Keyword(s):  
Wave Function ◽  
Uncertainty Principle ◽  
Functional Dependence ◽  
Phenomenological Theory ◽  
Stationary Wave ◽  
Smoluchowski Equation ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty ◽  
Proton Lifetime ◽  
Muon Decays

We present a Smoluchowski-like equation for subnuclear reactions which could be applied to both proton and muon decays. Combined with the Heisenberg uncertainty principle, this phenomenological theory gives the known functional dependence of the proton (muon) lifetimes on mp, Mx; (mμ, Mw), where mp(mμ) are proton (μ meson) rest masses and Mx(Mw) are the threshold masses for the electroweak/strong (electroweak) forces unification. The stationary wave function of the reactions is also obtained.

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