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Eigenstates with the auxiliary field method

Abstract : 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 relativistic 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 a two-body Schrödinger equation with a linear potential and show that very good approximations of the corresponding eigenstates can be obtained with the auxiliary field method.
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Contributor : Emmanuelle Vernay <>
Submitted on : Thursday, June 3, 2010 - 12:46:46 PM
Last modification on : Thursday, November 19, 2020 - 12:58:54 PM

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C. Semay, B. Silvestre-Brac. Eigenstates with the auxiliary field method. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2010, 43, pp.265302. ⟨10.1088/1751-8113/43/26/265302⟩. ⟨in2p3-00488905⟩

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