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Free Particle

  • Alessandro Teta
Chapter
Part of the UNITEXT for Physics book series (UNITEXTPH)

Abstract

We consider a free particle in \(\mathbb {R}^d\) and discuss the properties of the quantum dynamics. Using Fourier transform, we construct the Hamiltonian, describe the spectrum, derive the explicit formula for the unitary group, and characterize its asymptotic behavior for large times. We analyze the time evolution of a wave packet and give a quantitative description of the interference effect between two wave packets. Finally, we briefly discuss the dynamics of a particle subject to a constant force field.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di Matematica Guido CastelnuovoUniversità degli Studi di Roma “La Sapienza”RomeItaly

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