Open Access
March 2011 Further Developments for the Auxiliary Field Method
Fabien Buisseret, Claude Semay, Bernard Silvestre-Brac
J. Phys. Math. 3: 1-8 (March 2011). DOI: 10.4303/jpm/P111101


The auxiliary field method is a technique to obtain approximate closed formulae for the solutions of both nonrelativistic and semirelativistic eigenequations in quantum mechanics. For a many-body Hamiltonian describing identical particles, it is shown that the approximate eigenvalues can be written as the sum of the kinetic operator evaluated at a mean momentum $p_0$ and of the potential energy computed at a mean distance $r_0$. The quantities $p_0$ and $r_0$ are linked by a simple relation depending on the quantum numbers of the state considered and are determined by an equation which is linked to the generalized virial theorem. The (anti)variational character of the method is discussed, as well as its connection with the perturbation theory. For a nonrelativistic kinematics, general results are obtained for the structure of critical coupling constants for potentials with a finite number of bound states.


Download Citation

Fabien Buisseret. Claude Semay. Bernard Silvestre-Brac. "Further Developments for the Auxiliary Field Method." J. Phys. Math. 3 1 - 8, March 2011.


Published: March 2011
First available in Project Euclid: 29 January 2013

zbMATH: 1264.81191
Digital Object Identifier: 10.4303/jpm/P111101

Primary: 81Q05

Keywords: Closed and approximate solutions to the Dirac equation , Closed and approximate solutions to the Klein-Gordon equation , Closed and approximate solutions to the Schrödinger equation , quantum theory

Rights: Copyright © 2011 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.3 • March 2011
Back to Top