Bernard Silvestre-Brac et al 2008 J. Phys. A: Math. Theor. 41 425301 doi:10.1088/1751-8113/41/42/425301
Bernard Silvestre-Brac1, Claude Semay2 and Fabien Buisseret2
Show affiliationsIt has recently been shown that the auxiliary field method is an interesting tool to compute approximate analytical solutions of the Schrödinger equation. This technique can generate the spectrum associated with an arbitrary potential V(r) starting from the analytically known spectrum of a particular potential P(r). In the present work, general important properties of the auxiliary field method are proved, such as scaling laws and independence of the results on the choice of P(r). The method is extended in order to find accurate analytical energy formulae for radial potentials of the form aP(r) + V(r), and several explicit examples are studied. Connections existing between the perturbation theory and the auxiliary field method are also discussed.
81Txx Quantum field theory; related classical field theories (See also 70Sxx)
Issue 42 (24 October 2008)
Received 13 June 2008, in final form 27 August 2008
Published 22 September 2008
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