Exact solutions of the Schrödinger equation for an anharmonic potential in two dimensions

Within the framework of ansatz method, we investigate the exact closed-form solutions of the time independent Schrödinger equation for a two - dimensional anharmonic potential having sextic-type anharmonicity [say V(x,y)=∑i,j=06aijxiyj, with 1 ⩽ i + j ⩽ 6]. By imposing few restrictions on ansatz parameters and at the cost of some constraints on potential parameters, the ground state as well as excited states solutions are obtained.