How does quantum impenetrability affect Aharonov-Bohm scattering?

On the boundary conditions for the Dirac equation

“…In section 2 we give several physically acceptable boundary conditions, some of which were already proposed in scattering problems [4,5]. We find nontrivial solutions of the Dirac equation for a particle with a fixed mass localized in a box.…”

“…In fact, by changing the boundary conditions of a given operator, one modifies the operator itself without changing its formal expression, not to mention the risk of losing the self-adjointness property (see appendix A). For example, in the Aharonov-Bohm effect, by choosing different boundary conditions, which preserve self-adjointness, one obtains different cross sections [4]; aside from other considerations, it is the experimental arrangement which selects the appropriate observable.…”

Topological Effects in Quantum Mechanics

“…In the special gauge the VP of a TS with its axis parallel to the z axis is [18,24,126] However, we are unable to evaluate the integral (6.28) along an arbitrary closed curve.…”

“…Theoretically But first we recall the situation for the usual static magnetic toroidal solenoid without a double charged layer [24,126]. In this case: The VP can not be removed from this equation by a gauge transformation and this leads to a shift of the interference pattern on the screen installed behind the TS.…”

General boundary conditions for a Dirac particle in a box and their non-relativistic limits

“…Moreover, different BCs lead to different physical consequences. For relativistic scattering problems [6,9], it has been proposed that the vanishing of only the large component of the Dirac spinor is a physically acceptable BC. It can be easily seen that, for the 'free' particle in a box, in the non-relativistic limit this BC yields the well known Dirichlet BC.…”