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Physics Letters A

On the one-dimensional Coulomb problem

Benjamín Raziel Jaramillo Avila, R. P. Martı́nez-y-Romero, H. N. Núñez‐Yépez, A. L. Salas‐Brito

Published Oct 31, 2009• 24 citations
Publisher
DOI
10.1016/j.physleta.2009.10.073

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A set of generalized coherent states for the one-dimensional Coulomb problem in coordinate representation is constructed. At first, we obtain a mapping for proper transformation of the one-dimensional Coulomb problem into a nonrotating four-dimensional isotropic harmonic oscillator in the hyperspherical space, and the generalized coherent states for the one-dimensional Coulomb problem is then obtained in exact closed form. This exactly soluble model can provide an adequate means for a quantum coherency description of the Coulomb problem in one dimension, sample for coherent aspects of the exciton model in one-dimension example in high-temperature superconductivity, semiconductors, and polymers. Also, it can be useful for investigating the coherent scattering of the Coulomb particles in one dimension.