Saturation in heavy quarkonia spectra with energy-dependent confining potential in N-dimensional space

We study the energy spectra of Schriidinger Hamiltonian in N-dimensional space with Coulomb plus inverse quadratic term V(r) = -alpha/r + g/r(2) and energy-dependent confining potential of the form a(E)r + b(E)r(2). It is found that the energy spectra exhibit saturation effect, where these spectra are suppressed to finite values at large quantum numbers n and/or l at any dimensional space N. As a typical application, we obtained a compact mass formula for the spectra of heavy quarkonia (c<(<b>c)over bar> b<(<b>b)over bar>). It is found that the model is capable of reproducing the mass spectra of these systems with observed saturation governed by a factor gamma. The comparison of this work predictions with available experimental data as well as other relevant theoretical works is also presented. The eigenfunctions are expressed in terms of the bi-confluent Heun functions.