  An analytic solution of the N-dimensional radial Schr\"odinger equation with
the mixture of vector and scalar potentials via the Laplace transformation
method (LTM) is studied. The present potential is extended to include the spin
hyperfine, spin-orbit and tensor interactions. The energy eigenvalues and the
corresponding eigenfunctions have been determined in the N-dimensional space.
The present results are employed to study the different properties of the
heavy-light mesons. The masses of the scalar, vector, pseudoscalar and
pseudovector of B, Bs, D and Ds mesons have been calculated in the three
dimensional space. The effect of the dimensional number space is studied on the
masses of the heavy-light mesons. We find that the meson mass increases with
increasing dimensional space. The decay constants of the pseudoscalar and
vector mesons have been computed. In addition, the leptonic decay widths and
branching ratio for the B+, D+ and Ds+ mesons have been studied. Therefore, the
present method with the present potential gives good results which are in good
agreement with experimental data and are improved in comparison with recently
theoretical works.
