Analysis of N-dimensional Klein-Gordon equation for hydrogen molecule in the non-central potential field

We investigate a complete normalized relativistic solutions for N-dimensional Hartmann potential and relativistic effects of non-central potential field for hydrogen molecule within the framework of asymptotic iteration approach. We also discuss in detail the influence of dimensions on the angular probability distribution of hydrogen molecule. N-dimensional bound state wavefunction solutions including angular and radial solutions are expressed in terms of the Jacobi and Laguerre polynomials, respectively. N-dimensional angular wavefunctions of hydrogen molecule were visualized with Matlab software. In hyperspherical coordinates, the recurrence relations between diagonal matrix elements have been derived for N-dimensional Hartmann potential in relativistic theory. We also obtain analytical expressions of diagonal matrix elements and the recurrence formula between off-diagonal matrix elements in N-dimensions.