Feynman Paths, Sticky Walls, White Noise

Ludwig Streit

Benjamin Bähr, Boris Lemmer, Rina Piccolo

Christopher Casenas Bernido, M. Victoria Carpio-Bernido

Using the Streit–Hida formulation where the Feynman path integral is realized in the framework of white noise analysis, we evaluate the quantum propagator for systems with boundaries and topological constraints. In particular, the Feynman integrand is given as generalized white noise functionals for systems with flat wall boundaries and periodic constraints. Under a suitable Gauss–Fourier transform of these functionals the quantum propagator is obtained for: (a) the infinite wall potential; (b) a particle in a box; (c) a particle constrained to move in a circle; and (d) the Aharonov–Bohm system. The energy spectrum and eigenfunctions are obtained in all four cases.

Pavel Exner

Martin Grothaus, Anna Vogel, Christopher Casenas Bernido +1 more

In this note the concepts of path integrals and techniques how to construct them are presented. Here we concentrate on a White Noise approach. Combining White Noise techniques with a generalized time‐dependent Doss' formula Feynman integrands are constructed as white noise distributions beyond perturbation theory.

Debashis Gangopadhyay, Dipankar Home