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

Abstract

Abstract The bound-state solution of the radial Klein-Gordon equation has been obtained under the interaction of an exponential-type and Yukawa potential functions. The Greene-Aldrich approximation has been used to overcome the centrifugal barrier and enable the analytical solutions of the energy and wave functions in closed form. The momentum space wave function in D dimensions has been constructed using the Fourier transform. The mean values have been conjectured for the position and momentum spaces using two equivalent equations. The effects of the potential parameters on the expectation values and quantum information measurement have been investigated. For the 1D case, the results obey the Heisenberg uncertainty principle, Fisher, Shannon, Onicescu, and the Rényi entropic inequalities. Other information complexities measures, such as Shannon Power, Fisher-Shannon, and Lopez-Ruiz-Mancini-Calbet, have been verified. For the ground state, the 1D momentum expectation value $$\langle p^{2} \rangle_{00}$$ coincides with the 3D $$\langle p^{2} \rangle_{000}$$ values, which is an indication of degeneracy. The total energy of a particle in both 1D and 3D space may be degenerate due to the inter-dimensional degeneracy of the quantum numbers. However, in this present result, the degeneracy in 1D and 3D occurred for fixed quantum states at different momentum intervals. Thus, in 1D, a particle may transit an entire space ( $$\:-\infty\:<p<\infty\:)$$ with a certain kinetic energy, which must be equal to its kinetic energy if it moves through the interval $$\:0<p<\infty\:$$ in 3D space. This may have implications for kinetic energy degeneracy in higher dimensions.

Keywords

• Radial Klein-Gordon equation
• Shannon Entropy
• Renyi entropy
• Fisher information
• Kinetic energy