Free Fall of a Quantum Many-Body System

Fuente: arXiv
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Autores principales: Colcelli, Andrea, Mussardo, Giuseppe, Sierra, German, Trombettoni, Andrea
Formato: Preprint
Publicado: 2020
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author Colcelli, Andrea
Mussardo, Giuseppe
Sierra, German
Trombettoni, Andrea
author_facet Colcelli, Andrea
Mussardo, Giuseppe
Sierra, German
Trombettoni, Andrea
contents The quantum version of the free fall problem is a topic often skipped in undergraduate quantum mechanics courses because its discussion usually requires wavepackets built on the Airy functions -- a difficult computation. Here, on the contrary, we show that the problem can be nicely simplified both for a single particle and for general many-body systems by making use of a gauge transformation that corresponds to a change of reference frame from the laboratory frame to the one comoving with the falling system. Using this approach, the quantum mechanics problem of a particle in an external gravitational potential reduces to a much simpler one where there is no longer any gravitational potential in the Schrödinger equation. It is instructive to see that the same procedure can be used for many-body systems subjected to an external gravitational potential and a two-body interparticle potential that is a function of the distance between the particles. This topic provides a helpful and pedagogical example of a quantum many-body system whose dynamics can be analytically described in simple terms.
format Preprint
id arxiv_https___arxiv_org_abs_2009_03744
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Free Fall of a Quantum Many-Body System
Colcelli, Andrea
Mussardo, Giuseppe
Sierra, German
Trombettoni, Andrea
General Physics
Quantum Physics
The quantum version of the free fall problem is a topic often skipped in undergraduate quantum mechanics courses because its discussion usually requires wavepackets built on the Airy functions -- a difficult computation. Here, on the contrary, we show that the problem can be nicely simplified both for a single particle and for general many-body systems by making use of a gauge transformation that corresponds to a change of reference frame from the laboratory frame to the one comoving with the falling system. Using this approach, the quantum mechanics problem of a particle in an external gravitational potential reduces to a much simpler one where there is no longer any gravitational potential in the Schrödinger equation. It is instructive to see that the same procedure can be used for many-body systems subjected to an external gravitational potential and a two-body interparticle potential that is a function of the distance between the particles. This topic provides a helpful and pedagogical example of a quantum many-body system whose dynamics can be analytically described in simple terms.
title Free Fall of a Quantum Many-Body System
topic General Physics
Quantum Physics
url https://arxiv.org/abs/2009.03744