A HILL-DETERMINANT APPROACH TO SYMMETRICAL DOUBLE-WELL POTENTIALS IN 2 DIMENSIONS

Energy levels of the Schrodinger equation for a double-well potential V(x,y; Z(2),lambda) = -Z(2)[x(2) + y(2)] + lambda[alpha(xx)x(4) + 2 al pha(xy)x(2)y(2) + alpha(yy)y(4)] in two-dimensional space are calculat ed, using a Hill-determinant approach for several eigenstates and a ra nge of values of lambda and Z(2). Special emphasis is placed on the la rger values of Z(2), for which the eigenvalues for different states ha ve almost degenerate eigenvalues.