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

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

1998-03-10

arxiv.org/abs/quant-ph/9803020v3

Physics Letters A 248 (1998) 285-289

Physics

Quantum Physics

4 pages ReVTeX 4 epsf figures included, correction expanded refs

Scientific paper

10.1016/S0375-9601(98)00725-7

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, $\delta'$ potential, non-trivial topology in quantum mechanics, exotic wave-function aholonomy

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