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Eigensolution techniques, expectation values and Fisher information of Wei potential function.

C A Onate1, M C Onyeaju2, D T Bankole3

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Researchers solved the Klein-Gordon equation with a new Wei potential. They analyzed Fisher information and found parameter variations sometimes violate Heisenberg uncertainty, but quantum numbers obey it.

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Area of Science:

  • Theoretical Physics
  • Quantum Mechanics
  • Relativistic Quantum Mechanics

Background:

  • The Klein-Gordon equation describes relativistic spin-zero particles.
  • The Wei potential is a model for interatomic interactions.
  • Fisher information quantifies information about a parameter in a statistical model.

Purpose of the Study:

  • To find an approximate solution for the one-dimensional relativistic Klein-Gordon equation with an improved Wei potential.
  • To investigate the Fisher information in position and momentum spaces.
  • To analyze the influence of Wei potential parameters and quantum numbers on Fisher information and its relation to the Heisenberg uncertainty principle.

Main Methods:

  • Obtained an approximate solution to the relativistic Klein-Gordon equation.
  • Derived the non-relativistic Schrödinger equation solution via mappings.
  • Calculated Fisher information using expectation values for position and momentum spaces.
  • Graphically analyzed the effects of Wei potential parameters, quantum number (n), and angular momentum quantum number (ℓ) on Fisher information.

Main Results:

  • The study successfully obtained approximate solutions for the Klein-Gordon and Schrödinger equations.
  • Fisher information was computed and its dependence on Wei potential parameters, n, and ℓ was examined.
  • Most Wei potential parameter variations against Fisher information did not adhere to the Heisenberg uncertainty relation for Fisher information.

Conclusions:

  • The variations of quantum number (n) and angular momentum quantum number (ℓ) on Fisher information were found to obey the Heisenberg uncertainty relation.
  • The study highlights the complex interplay between potential parameters, quantum numbers, and information-theoretic quantities in relativistic quantum systems.
  • The findings contribute to understanding the behavior of quantum systems under specific potentials and their adherence to fundamental uncertainty principles.