Quantum potentials with q-Gaussian ground states

• Published in: Physica A Vol. 391; no. 4; pp. 1068 - 1073
• Main Authors: Vignat, Christophe, Plastino, Angel, Plastino, Angel R., Dehesa, Jesus Sanchez
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.02.2012; Elsevier
• Subjects: [formula omitted]-Gaussian; Asymptotic properties; Computer Science; Coulomb potential; Engineering Sciences; Entropy; Ground state; Signal and Image processing; Spherically symmetrical quantum potentials; Statistical mechanics; Wavefunctions; q-Gaussian; Coulomb potential; Spherically symmetrical quantum potentials
• ISSN: 0378-4371; 0378-4371
• DOI: 10.1016/j.physa.2011.09.031

We determine families of spherically symmetrical D-dimensional quantum potential functions V(r) having ground-state wavefunctions that exhibit, either in configuration space or in momentum space, the form of an isotropic q-Gaussian. These wavefunctions admit a maximum-entropy description in terms of Sq power-law entropies. We show that the potentials with a ground state of the q-Gaussian form in momentum space admit the Coulomb potential −1/r as a particular instance. Furthermore, all these potentials behave asymptotically as the Coulomb potential for large r for all values of the parameter q such that 0<q<1. ► We advance new links between q-entropies and quantum mechanics. ► We present families of potentials with q-Gaussian ground states. ► We provide new evidence linking q-entropies with −1/r interactions.