Eigenstates with the auxiliary field method

Details Eigenstates with the auxiliary field method Eigenstates with the auxiliary field method

2010-01-11

arxiv.org/abs/1001.1706v2

J. Phys. A 43 (2010) 265302

Physics

Quantum Physics

Extended version published in J. Phys. A

Scientific paper

10.1088/1751-8113/43/26/265302

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 Schr\"odinger 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 Schr\"odinger 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 a very good accuracy in some cases.

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