Energy levels for a double-well potential in three-dimensional system using Hill determinant approach

Energy levels of the Schrödinger equation for the double-well potential V(x, y, z; λ, Z2) = − 12 Z2[x2 + y2 + z2] + 12 λ[axxx4 + ayyy4 + azzz4 + 2axyx2y2 + 2axzx2z2 + 2ayzy2z2] in a three-dimensional system are calculated using the Hill determinant approach for several eigenstates and large values of the perturbation parameters (λ and Z2). Emphasis is specially placed on the larger values of Z2, because the eigenvalues for different states have almost degenerate eigenvalues. Some of the results calculated by the Hill determinant approach are compared with the results produced by other techniques.