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Quantum Information Entropies on Hyperbolic Single Potential Wells.

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Summary
This summary is machine-generated.

This study explores quantum information entropies in hyperbolic potential wells. Researchers found that position and momentum entropies vary with potential width and depth, satisfying the BBM inequality.

Keywords:
hyperbolic potential wellposition and momentum Shannon entropiesquantum information entropy

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Area of Science:

  • Quantum Information Theory
  • Mathematical Physics

Background:

  • Hyperbolic potential wells are used in quantum mechanics to model various physical systems.
  • Understanding quantum information entropies is crucial for characterizing quantum states.

Purpose of the Study:

  • To investigate quantum information entropies (position and momentum) for two distinct hyperbolic potential wells.
  • To analyze the behavior of these entropies in relation to potential width and depth.

Main Methods:

  • Focusing on the wave functions of a moving particle within the potentials.
  • Illustrating the behaviors of position and momentum entropy densities.
  • Examining the variation of position entropy (Sx) and momentum entropy (Sp) with potential well depth (u).

Main Results:

  • Momentum entropy densities change with potential width.
  • Position entropy density magnitude decreases as momentum entropy magnitude increases.
  • The sum of position and momentum entropies (Sx + Sp) satisfies the BBM inequality for varying potential well depths.

Conclusions:

  • The study provides insights into the quantum information properties of hyperbolic potentials.
  • The findings confirm the robustness of the BBM inequality in these systems.
  • This research contributes to the understanding of entropy dynamics in quantum systems.