Two-dimensional noncommutative gravitational quantum well. (English) Zbl 1379.81051
Summary: In this paper we consider two kinds of noncommutative space-time commutation relations in two-dimensional configuration space and feature the absolute value of the minimal length from the generalized uncertainty relations associated to the particular commutation relations. We study the problem of the two-dimensional gravitational quantum well in new Hermitian variables and confront the experimental results for the first lowest energy state of the neutrons in the Earth’s gravitational field to estimate the upper bounds on the noncommutativity parameters. The absolute value of the minimum length is smaller than a few nanometers.
MSC:
| 81R60 | Noncommutative geometry in quantum theory |
| 81V17 | Gravitational interaction in quantum theory |
| 81S05 | Commutation relations and statistics as related to quantum mechanics (general) |
Keywords:
deformed algebras; minimal length; noncommutative quantum mechanics; gravitational quantum wellReferences:
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