Path integrals for boundaries in diffusion and quantum mechanics
| dc.contributor.advisor | Koch, Benjamin | |
| dc.contributor.author | Lantaño Pinto, Trinidad | |
| dc.contributor.other | Pontificia Universidad Católica de Chile. Instituto de Física | |
| dc.date | 2020-10-24 | |
| dc.date.accessioned | 2020-11-13T16:35:05Z | |
| dc.date.issued | 2020 | |
| dc.date.updated | 2020-11-08T19:39:29Z | |
| dc.description | Tesis (Master in Physics)--Pontificia Universidad Católica de Chile, 2020 | |
| dc.description.abstract | 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. | |
| dc.description.version | 2020-10-24 | |
| dc.format.extent | iii, 52 páginas | |
| dc.identifier.doi | 10.7764/tesisUC/FIS/48240 | |
| dc.identifier.uri | https://doi.org/10.7764/tesisUC/FIS/48240 | |
| dc.identifier.uri | https://repositorio.uc.cl/handle/11534/48240 | |
| dc.language.iso | en | |
| dc.nota.acceso | Contenido completo | |
| dc.rights | acceso abierto | |
| dc.subject.ddc | 530.12 | |
| dc.subject.dewey | Matemática física y química | es_ES |
| dc.subject.other | Integrales de trayectoria | es_ES |
| dc.subject.other | Teoría cuántica | es_ES |
| dc.subject.other | Operador de Schrodinger | es_ES |
| dc.title | Path integrals for boundaries in diffusion and quantum mechanics | es_ES |
| dc.type | tesis de maestría | |
| sipa.codpersvinculados | 1006903 |