The energy levels for a symmetric and nonsymmetric double-well potential in a two-dimensional system using the Hill determinant approach

Abstract

Energy levels of the Schrödinger equation for a double-well potentialV(x, y; Z _x ², Z_y ²,λ) = −Z _x ² x ² -Z _y ² y ² +λ[a _xx x ⁴ + 2a _xy ^x2y2 +a _yy y ⁴] in a two-dimensional system are calculated using the Hill determinant approach for several eigenstates and over a wide range of values of the perturbation parameters (λ, Z _x ²,Z _y ²). Some of the results calculated by the Hill determinant approach are compared with those results produced by the inner product technique.