Double Spiral Energy Surface in One-dimensional Quantum Mechanics of Generalized Pointlike Potentials
Abstract
Description
We analyze the eigenvalue problem of a quantum particle on the line with the generalized pointlike potential of three parameter family. It is shown that the energy surface in the parameter space has a set of singularities, around which different eigenstates are connected in the form of paired spiral stairway. An examplar wave-function aholonomy is displayed where the ground state is adiabatically turned into the second excited state after cyclic rotation in the parameter space.
KEYWORDS: one-dimensional system, $δ'$ potential, non-trivial topology in quantum mechanics, exotic wave-function aholonomy
4 pages ReVTeX 4 epsf figures included, correction expanded refs
4 pages ReVTeX 4 epsf figures included, correction expanded refs