Essentials of the Entropic Uncertainty Relations and Measurement of Fisher-Shannon Product of a Free Particle in Three Dimensions | Chapter 3 | Fundamental Research and Application of Physical Science Vol. 2

 The purpose concerning this article search out calculate the numerical principles of the Shannon (S) and Fisher (I) information entropies in addition to their Shannon power (J) and Fisher-Shannon commodity (P) for a free particle in three dimensions. In two together coordinate and momentum scope, the numerical principles have been planned for various values of the cubical box's distance (L). Further, the validity of the entropic changeableness relations in the way that the Bialynicki-Birula and Myceilski (BBM) inequality relation, Stam-Cramer-Rao prejudices (better known as the Fisher located uncertainty connection) and the Fisher-Shannon product relation have happened investigated. The Fisher-Shannon amount has been received and analyzed, that can be considered as a new equating measure. The article is fundamentally based on the idea, measurements and on the behaviour of the Shannon entropy, Fisher facts entropy, Shannon capacity and the Fisher-Shannon product. Here, the plane wave resolution of the free particle in three dimensions is deliberate and the wave function is normalized in an arbitrarily big but finite hexahedron. The Fourier transforms of the coordinate scope wave function provided the momentum scope wave function. The probability densities matching to the respective wave functions have happened employed to compute the mathematical values of the facts theoretic quantities to a degree Shannon entropy, Fisher entropy, Shannon capacity and the Fisher-Shannon product two together in the coordinate and momentum room and the computed values have happened presented in the respective tables. Finally, the entropic doubt relations examined have been raise consistently satisfying the matching inequalities to a degree Bialynicki-Birula and Mycielski (BBM) inequality, the Stam-Cramer-Rao prejudices and the Fisher-Shannon product relation. The study demonstrates the validity of the entropic changeableness relations for the motion of a free piece in three dimensions.

Author(s) Details:

Sudin Singh,
Department of Physics, Bolpur College, Bolpur, Birbhum, Pin-731204, W.B., India.

Please see the link here: https://stm.bookpi.org/FRAPS-V2/article/view/10144