Klein–Gordon particles in mixed vector–scalar inversely linear potentials

Abstract

The problem of a spinless particle subject to a general mixing of vector and scalar inversely linear potentials in a two-dimensional world is analyzed. Exact bounded solutions are found in closed form by imposing boundary conditions on the eigenfunctions which ensure that the effective Hamiltonian is Hermitian for all the points of the space. The nonrelativistic limit of our results adds a new support to the conclusion that even-parity solutions to the nonrelativistic one-dimensional hydrogen atom do not exist.

Bound States of the Klein-Gordon for Exponential-Type Potentials in D-Dimensions

“…2) In the non-relativistic approximation of the KG energy equation (potential energies small compared to 2 Mc and E Mc  Equation (32) reduces into the form [72]  In the non-relativistic limits, the energy spectrum is The un-normalized wave function corresponding to the energy levels is …”

Bound States of the Klein–gordon Equation for Vector and Scalar General Hulthén-Type Potentials in D-Dimension

“…On the other hand, it has been shown that when S 0 ≥ V 0 , there exist real bound state solutions (i.e., the radial wave function must satisfy the boundary condition that it becomes zero when r → ∞ and also finite at r = 0). However, there are very few exact solvable cases [15][16][17][18][19]. The bound state solutions for the last case is obtained for the s-wave Klein-Gordon equation with the exponential [15] and some other classes of potentials [16].…”

Relativistic solution in D-dimensions to a spin-zero particle for equal scalar and vector ring-shaped Kratzer potential

“…It is remarkable that in most works in this area, the scalar and vector potentials are taken to be almost equal (i.e., S = V ) [2,24]. However, in a few other cases, the case is considered where the scalar potential is greater than the vector potential (in order to guarantee the existence of Klein-Gordon bound states)  i.e., S > V [25][26][27][28][29][30]. Nonetheless, such physical potentials are very few.…”