HAL : in2p3-00564101, version 1
 arXiv : 1102.1321
 DOI : 10.1063/1.3589959
 Journal of Mathematical Physics 52 (2011) 052107
 Duality relations in the auxiliary field method
 (2011)
 The eigenenergies $\epsilon^{(N)}(m;\{n_i,l_i\})$ of a system of $N$ identical particles with a mass $m$ are functions of the various radial quantum numbers $n_i$ and orbital quantum numbers $l_i$. Approximations $E^{(N)}(m;Q)$ of these eigenenergies, depending on a principal quantum number $Q(\{n_i,l_i\})$, can be obtained in the framework of the auxiliary field method. We demonstrate the existence of numerous exact duality relations linking quantities $E^{(N)}(m;Q)$ and $E^{(p)}(m';Q')$ for various forms of the potentials (independent of $m$ and $N$) and for both nonrelativistic and semirelativistic kinematics. As the approximations computed with the auxiliary field method can be very close to the exact results, we show with several examples that these duality relations still hold, with sometimes a good accuracy, for the exact eigenenergies $\epsilon^{(N)}(m;\{n_i,l_i\})$.
 Thème(s) : Physique/Physique Quantique
 Lien vers le texte intégral : http://fr.arXiv.org/abs/1102.1321
 in2p3-00564101, version 1 http://hal.in2p3.fr/in2p3-00564101 oai:hal.in2p3.fr:in2p3-00564101 Contributeur : Emmanuelle Vernay <> Soumis le : Mardi 8 Février 2011, 08:28:50 Dernière modification le : Lundi 20 Juin 2011, 08:47:47