Relativistic bound state solutions and quantum information theory in D dimensions under exponential-type plus Yukawa...

Area of Science:

• Quantum Mechanics
• Theoretical Physics
• Mathematical Physics

Background:

• The Klein-Gordon equation describes relativistic quantum particles.
• Solving it with complex potentials, like combined exponential-Yukawa, is challenging due to the centrifugal barrier.
• Analytical solutions are crucial for understanding particle behavior and quantum properties.

Purpose of the Study:

• To obtain bound-state solutions for the radial Klein-Gordon equation with a combined exponential-type and Yukawa potential.
• To derive analytical expressions for energy eigenvalues and wave functions.
• To investigate quantum information measures and potential parameter effects.

Main Methods:

• The Greene-Aldrich approximation was employed to handle the centrifugal barrier.
• Analytical solutions for energy and wave functions were derived in closed form.
• Fourier transforms were used to construct momentum space wave functions in D dimensions.

Main Results:

• Analytical solutions for energy and wave functions were successfully obtained.
• The study verified quantum information inequalities (Heisenberg, Rényi, etc.) in 1D.
• A significant finding is the degeneracy of kinetic energy between 1D and 3D spaces for specific quantum states.

Conclusions:

• The Greene-Aldrich approximation provides an effective method for solving the radial Klein-Gordon equation with these potentials.
• The results demonstrate the validity of various quantum information measures and inequalities.
• The observed kinetic energy degeneracy suggests implications for particle behavior in higher dimensions.