Free Fall of a Quantum Many-Body System

• URL: http://arxiv.org/abs/2009.03744v2
• Date: Sun, 31 Jul 2022 10:24:46 GMT
• Title: Free Fall of a Quantum Many-Body System
• Authors: Andrea Colcelli, Giuseppe Mussardo, German Sierra, Andrea Trombettoni
• Abstract summary: We show that the problem can be nicely simplified both for a single particle and for general many-body systems. It is instructive to see that the same procedure can be used for many-body systems subjected to an external gravitational potential.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 Schr\"{o}dinger 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.

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