Finite density QCD at strong coupling

We study strong coupling QCD in the Hamiltonian formulation at finite density by using an ansatz which exactly diagonalizes an effective Hamiltonian to second order in field operators. The equation of motion is derived and used to obtain the vacuum energy density and the gap equation. Further exploiting the equation of motion we show that the interaction induces a contribution to the total chemical potential which is momentum dependent. We solve the gap equation self-consistently with the total chemical potential and calculate the chiral condensate and the quark number density to leading order in N_c. The order of chiral phase transition is found to depend on the choice of input parameters. We discuss how our formalism may be extended to study the nature of the confinement-deconfinement phase transition