We present bound state masses of the self-conjugate and
non-self-conjugate mesons in the context of the Schrödinger
equation taking into account the relativistic kinematics and the quark
spins. We apply the usual interaction by adding the spin dependent
correction. The hyperfine splittings for the 2S charmonium and 1S
bottomonium are calculated. The pseudoscalar and vector decay constants
of the Bc meson and the unperturbed radial wave function at
the origin are also calculated. We have obtained a local equation with a
complete relativistic corrections to a class of three attractive static
interaction potentials of the general form V(r) =
-Ar-β+κrβ+V0, with
β = 1, 1/2, 3/4 which can also be decomposed into scalar and vector
parts in the form VV(r) =
-Ar-β+(1-ɛ)κrβ and
VS(r) = ɛκrβ+V0
where 0≤ɛ≤1. The energy eigenvalues are carried out up to
the third order approximation using the shifted large-N-expansion
technique.
Journal
Title
International Journal of Modern Physics A, Volume 20, Issue 17, pp. 4035-4054