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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