Tesis (Master in Physics)--Pontificia Universidad Católica de Chile, 2020 ; Diffusion and quantum mechanics with boundary conditions arise naturally in various situations in physics. While reflecting and absorbing boundaries are well mathematically described, intermediate scenarios are not that clear. Consider a reflective boundary which is removed for a time δ and subsequently reinstated. First, we place a Brownian particle at one side of this barrier and study its path-integral propagator. We obtained a closed expression for the particle’s probability of being before or after the barrier at a certain time. We then consider the same barrier, but when the removing time is unforeseen, so the particle could cross to the other side at some time within a known interval [0,T]. A path-integral propagator is computed, and it is shown numerically that the limit to the exact path integral is convergent. Finally, we consider a quantum particle in the presence of a reflective barrier removed at t = ∆t1 for a time δ and then reinstated. We propose a path-integral propagator for this process and show that the corresponding wave function satisfies the Schrodinger equation. ; 2020-10-24