  In this article, we employed the Quasi-particle debye mass at finite baryonic
chemical potential which can be used in the medium modified heavy quark
potential to solve the N-dimensional Schroedinger equation. The bound state
solution of the Schroedinger equation using Cornell potential is obtained by
Super-Symmetry Quantum Mechanics (SUSYQM) method. The thermodynamical
properties of quark matter is calculated by using baryonic chemical potential
(mu). We found that the binding energy of quarkonia dissociates more with
quasi-particle debye mass in comparison to non-perturbative and leading order
debye mass. The medium modified form of potential (real part) has been used to
study the thermodynamical properties of quark matter with different equation of
states (EoS) (i.e., pressure, energy density and speed of sound) with {mu}. The
mass spectra of quarkonia has been also calculated in the N-dimensional space,
and compared with the experimental data at N=3. We have also calculated the
dissociation temperature (T_D) for the ground states of quarkonium using the
dissociation criteria of thermal width.
