CONSTRUCTION OF EXACTLY SOLUBLE DOUBLE-WELL POTENTIALS

Solving the tunneling problem in a double-well potential requires knowing the wave function not just of the ground state, but also of the first excited state. A method is described that allows one to construct potentials together with these two wave functions. No approximations are made. To illustrate the method several examples are given. These include potentials that either diverge for large x or become asymptotically flat, with one or two wells, which may be symmetric or asymmetric. © 1995 The American Physical Society.