Free Fall of a Quantum Many-Body System
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866914838109749248 |
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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 |