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2010-06-02 - Article/Dans un journal avec peer-review - Anglais - 22 page(s)

Semay Claude , Silvestre-Brac B., "Eigenstates with the auxiliary field method" in Journal of Physics: A Mathematical and General, 43, 265302 (22 p.)

  • Edition : Institute of Physics Publishing (United Kingdom)
  • Codes CREF : Physique théorique et mathématique (DI1210), Mécanique quantique classique et relativiste (DI1211)
  • Unités de recherche UMONS : Physique nucléaire et subnucléaire (S824)
  • Instituts UMONS : Institut de Recherche sur les Systèmes Complexes (Complexys)
  • Centres UMONS : Algèbre, Géométrie et Interactions fondamentales (AGIF)
Texte intégral :

Abstract(s) :

(Anglais) The auxiliary field method is a powerful technique to obtain approximate closed-form energy formulas for eigenequations in quantum mechanics. Very good results can be obtained for Schrödinger and semirelativistic Hamiltonians with various potentials, even in the case of many-body problems. This method can also provide approximate eigenstates in terms of well-known wavefunctions, for instance harmonic oscillator or hydrogen-like states, but with a characteristic size which depends on quantum numbers. In this paper, we consider two-body Schrödinger equations with linear, logarithmic and exponential potentials and show that analytical approximations of the corresponding eigenstates can be obtained with the auxiliary field method, with very good accuracy in some cases.

Identifiants :
  • DOI : 10.1088/1751-8113/43/26/265302
  • arXiv : 1001.1706 [quant-ph]