Physical Sciences and Mathematics Commons^™

Quantum Mechanics Of Multi-Prong Potentials, Asim Gangopadhyaya, A Pagnamenta, Uday P. Sukhatme

Physics: Faculty Publications and Other Works

We describe the bound state and scattering properties of a quantum mechanical particle in a scalar N-prong potential. Such a study is of special interest since these situations are intermediate between one and two dimensions. The energy levels for the special case of N identical prongs exhibit an alternating pattern of non-degeneracy and (N−1) fold degeneracy. It is shown that the techniques of supersymmetric quantum mechanics can be used to generate new solutions. Solutions for prongs of arbitrary lengths are developed. Discussions of tunneling in N-well potentials and of scattering for piecewise constant potentials are given. Since our treatment is …