Propagators in quantum mechanics on multiply connected spaces

Michael G. G. Laidlaw

Eric A. Carlen, Maria I. Loffredo

Fabrizio Colombo, Elodie Pozzi, Irene Sabadini +1 more

The path-integral technique in quantum mechanics provides an intuitive framework for comprehending particle propagation and scattering. Calculating the propagator for the Aharonov-Bohm potential fits into the range of potentials in multiply-connected spaces, with the propagator represented through a series expansion. In this paper, we analyze the Schrödinger evolution of superoscillations, showing the supershift properties of the solution to the Schrödinger equation for this potential. Our proof is based on the continuity of particular infinite order differential operators acting on spaces of entire functions.

Albino Hernández-Galeana, J. M. Rivera-Rebolledo, José Luis López-Bonilla +1 more

B. G. Sidharth

t is well known that the difference between Quantum Mechanics and Classical Theory appears most crucially in the non Classical spin half of the former theory and the Wilson-Sommerfelt quantization rule. We argue that this is symptomatic of the fact that Quantum Theory is actually a theory in multiply connected space while Classical Theory operates in simply connected space.