A Study on the Scattering of Matter Waves through Slits

TL;DR

This paper investigates matter wave scattering through multiple slits using the Feynman Path Integral formalism, revealing complex interference patterns, transition regions, and controllable quasi-traps in the probability density distribution.

Contribution

It introduces a detailed analysis of near-zero probability densities and pattern transitions in matter wave scattering through slits, including hypergeometric function expressions.

Findings

Braid-like interference patterns in double slits

Transition from braided to fringe-like structures

Existence of controllable quasi-traps smaller than the wavelength

Abstract

Scattering of matter waves through slits has been explored using the Feynman Path Integral formalism. We explicitly plot the near-zero probability densities to analyse the behaviour near the slit. Upon doing so, intriguing patterns emerge, most notably the braid-like structure in the case of double slits, whose complexity increases as one increases the number of slits. Furthermore, the plot shows the existence of a transition region, where the distribution of near-zero probability points changes from the braided to the fringe-like structure, which has been analysed by explicitly expressing the wavefunction as a hypergeometric function. These patterns are analysed while considering the continuity equation and its consequences for the regions with zero probability density. As a result, we find quasi-traps in the region whose size can be controlled and made much smaller than the wavelength of matter waves.