Quantum-mechanical examples have been constructed of local potentials with bound eigenstates embedded in the dense continuum of scattering states. The method employed corrects and extends a procedure invented by von Neumann and Wigner. Cases are cited whereby deformation of the local potential causes the continuum bound state to move downward through the bottom of the continuum, and to connect analytically to a nodeless ground state. A doubly excited model atom is also displayed, with interactions between its two "electrons," having an infinite lifetime (in the Schrödinger equation regime). In the light of these examples, attention is focused on quantitative interpretation of real tunneling phenomena, and on the existence of continuum bound states in atoms and molecules.

• Received 5 November 1974

DOI:https://doi.org/10.1103/PhysRevA.11.446