BOUND-STATES IN THE CONTINUUM FROM SUPERSYMMETRIC QUANTUM-MECHANICS

Starting from a potential with a continuum of energy eigenstates, we s how how the methods of supersymmetric quantum mechanics can be used to generate families of potentials with bound states in the continuum (B IC's). We also find the corresponding wave functions. Our method prese rves the spectrum of the original potential except it adds these discr ete BIC's at selected energies. Specifically, we compute and graph pot entials which have bound states in the continuum starting from a null potential representing a free particle and from both the attractive an d the repulsive Coulomb potentials.