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arXiv · 2009.03744

Free Fall of a Quantum Many-Body System

Andrea Colcelli·Giuseppe Mussardo·German Sierra·Andrea Trombettoni
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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 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.

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Andrea Colcelli, Giuseppe Mussardo, German Sierra, Andrea Trombettoni. 2022-07-31. Free Fall of a Quantum Many-Body System. https://doi.org/10.1119/10.0013427

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