Harmonic states for the free particle
Abstract
Different families of states, which are solutions of the time-dependent free Schr\"odinger equation, are imported from the harmonic oscillator using the Quantum Arnold Transformation introduced in a previous paper. Among them, infinite series of states are given that are normalizable, expand the whole space of solutions, are spatially multi-localized and are eigenstates of a suitably defined number operator. Associated with these states new sets of coherent and squeezed states for the free particle are defined representing traveling, squeezed, multi-localized wave packets. These states are also constructed in higher dimensions, leading to the quantum mechanical version of the Hermite-Gauss and Laguerre-Gauss states of paraxial wave optics. Some applications of these new families of states and procedures to experimentally realize and manipulate them are outlined.
Cite
@article{arxiv.1010.5525,
title = {Harmonic states for the free particle},
author = {Julio Guerrero and Francisco F. López-Ruiz and Victor Aldaya and Francisco Cossio},
journal= {arXiv preprint arXiv:1010.5525},
year = {2015}
}
Comments
21 pages, 3 figures. Title changed, content added, references added