Bound states correspond to . It follows that . For the Schrödinger equation becomes

where . Thus for , and applying we conclude . For the Schrödinger equation is

where . Thus for . For odd solutions, , hence

thus, by continuity we have and by smoothness we have . Thus Let and . Since , it follows , hence

which may be solved numerically. A similar treatment for the even case¹ gives the result stated above.