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arXiv · 1904.06597

Effective Quantum Mechanics of a falling particle

Guillermo Chacon-Acosta·Hector Hernandez-Hernandez·Mercedes Velazquez
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Abstract

We analyze the problem of one dimensional quantum particle falling in a constant gravitational field, also known as the {\it bouncing ball}, employing a semiclassical approach known as momentous effective quantum mechanics. In this formalism the quantum evolution is described through a dynamical system of infinite dimension for the position, the momentum and all dispersions. Usually the system is truncated to have a finite dimensional one, however, in this case equations of motion decouple and the system can be solved. For a specific set of initial conditions we find that the time dependent dispersion in position is always around the classical trajectory.

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Guillermo Chacon-Acosta, Hector Hernandez-Hernandez, Mercedes Velazquez. 2019-04-13. Effective Quantum Mechanics of a falling particle. https://arxiv.org/abs/1904.06597

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