Double Spiral Energy Surface in One-dimensional Quantum Mechanics of Generalized Pointlike Potentials

Abstract

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, ${\delta }^{\prime }$ potential, non-trivial topology in quantum mechanics, exotic wave-function aholonomy

4 pages ReVTeX 4 epsf figures included, correction expanded refs

References in corpus (1)

• Realizing Discontinuous Wave Functions with Renormalized Short-Range Potentials

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