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Quantum potentials with q-Gaussian ground states

Author

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  • Vignat, Christophe
  • Plastino, Angel
  • Plastino, Angel R.
  • Dehesa, Jesus Sanchez

Abstract

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

Suggested Citation

  • Vignat, Christophe & Plastino, Angel & Plastino, Angel R. & Dehesa, Jesus Sanchez, 2012. "Quantum potentials with q-Gaussian ground states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1068-1073.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:4:p:1068-1073
    DOI: 10.1016/j.physa.2011.09.031
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    Cited by:

    1. Alves, L.G.A. & Ribeiro, H.V. & Santos, M.A.F. & Mendes, R.S. & Lenzi, E.K., 2015. "Solutions for a q-generalized Schrödinger equation of entangled interacting particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 35-44.
    2. Puertas-Centeno, D., 2019. "Differential-escort transformations and the monotonicity of the LMC-Rényi complexity measure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 177-189.
    3. Sekania, Michael & Appelt, Wilhelm H. & Benea, Diana & Ebert, Hubert & Vollhardt, Dieter & Chioncel, Liviu, 2018. "Scaling behavior of the Compton profile of alkali metals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 489(C), pages 18-27.

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