It is shown that for the double-well potential three similarly constructed pairs of solutions of the Schrödinger equation can be derived which are such that they can be linked in regions of common validity. Evaluating the boundary conditions satisfied by the even and odd wave functions at a minimum, several analogous transcendental equations are obtained from which the splitting of (asymptotically degenerate) eigenvalues can be deduced.

• Received 21 September 1981

DOI:https://doi.org/10.1103/PhysRevD.25.1552