Volome Charge Density in Mixed Number Lorentz Transformation

Bhuiyan, S. A.

doi:10.3329/jsr.v11i2.39632

Cited by 3 publications

(2 citation statements)

References 4 publications

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“…In this paper, the interest is concentrated only on the Shannon information entropy (S). Information entropy is subject characterized by the charge density [9] or the probability density of the system corresponding to changes in some observable such that the higher the probability density lower is the information. So, the lower the entropy is, the more concentrated is the wave function.…”

Section: Introductionmentioning

confidence: 99%

Shannon Information Entropy Sum of a Free Particle in Three Dimensions Using Cubical and Spherical Symmetry

Singh¹,

Saha

2023

J. Sci. Res.

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In this paper, the plane wave solutions of a free particle in three dimensions for Cubical and Spherical Symmetry have been considered. The coordinate space wave functions for the Cubical and Spherical Symmetry are obtained by solving the Schrdinger differential equation. The momentum space wave function is obtained by using the operator form of an observable in the case of Cubical Symmetry. For Spherical Symmetry, the same is obtained by taking the Fourier transform of the respective coordinate space wave function. The wave functions have been used to constitute probability densities in coordinate and momentum space for both the symmetries. Further, the Shannon information entropy has been computed both in coordinate and momentum space respectively for (L is the length of the side of the cubical box) values for Cubical Symmetry and for values in Spherical Symmetry keeping (k is the wave vector and p is the momentum of the free particle) constant. The values obtained for the Shannon information entropies are found to satisfy the Bialynicki-Birula and Myceilski (BBM) inequality at larger values () in case of Cubical Symmetry and for values of and in Spherical Symmetry.

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Section: Introductionmentioning

confidence: 99%

Shannon Information Entropy Sum of a Free Particle in Three Dimensions Using Cubical and Spherical Symmetry

Singh¹,

Saha

2023

J. Sci. Res.

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“…Shannon connected the measure of the information content with probability density. It is necessary to mention that Shannon information entropy (S) and Fisher information entropy (I) [18] are both characterized by probability density or the charge density corresponding to changes in some observables [19]. The two most important entropic measures of the information theories are the Shannon information entropy (S) and Fisher information entropy (I) [20,21].…”

Section: Introductionmentioning

confidence: 99%

A Theoretical Study on Wave Packet Dynamics Using Information Theory

Singh,

Saha

2023

J. Sci. Res.

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The article intertwines the study of wave packet dynamics with information-theoretic measurements in one dimensional (D =1) system. A localized wave packet at time t=0 has been considered here and its change at later instant of time t is calculated for the position space wave function. The momentum space wave function is obtained by taking the Fourier transform of the position space wave function at time t= 0 . These wave functions are then employed to construct the wave packet's respective probability densities in position and momentum space, and later have been used to compute the corresponding position and momentum space Shannon (S) and Fisher information (I) entropies. It has been observed that although the Shannon and Fisher information entropies explicitly depend on the standard deviation, neither the Shannon entropy sum nor the product of Fisher information entropies is. Moreover, for D dimensional systems, the computed values of the Shannon and Fisher entropies are found to satisfy the lower bounds of the Bialynicki-Birula and Myceilski (BBM) inequality relation and the Stam-Cramer-Rao inequalities better known as the Fisher based uncertainty relation. Thus, our theoretical study explores the validation of information-theoretic measurements for wave packet dynamics using the basic formulations of information theory.

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Volume Charge Density in Geometric Product Lorentz Transformation

Alam¹,

Baizid²

2021

J. eng. adv.

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Lorentz Transformation is the relationship between two different coordinate frames time and space when one inertial reference frame is relative to another inertial reference frame with traveling at relative speed. In this paper, we have derived the transformation formula for the volume charge density in Geometric Product Lorentz Transformation. The changes of volume charge density of moving frame in terms of that rest frame in Geometric Product Lorentz Transformation at various velocities and angles were studied as well.

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Volome Charge Density in Mixed Number Lorentz Transformation

Cited by 3 publications

References 4 publications

Shannon Information Entropy Sum of a Free Particle in Three Dimensions Using Cubical and Spherical Symmetry

Shannon Information Entropy Sum of a Free Particle in Three Dimensions Using Cubical and Spherical Symmetry

A Theoretical Study on Wave Packet Dynamics Using Information Theory

Volume Charge Density in Geometric Product Lorentz Transformation

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