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Journal Articles Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Year : 2007

Few-body problem in terms of correlated gaussians

Abstract

In their textbook, Suzuki and Varga [Y. Suzuki and K. Varga, {\em Stochastic Variational Approach to Quantum-Mechanical Few-Body Problems} (Springer, Berlin, 1998)] present the stochastic variational method in a very exhaustive way. In this framework, the so-called correlated gaussian bases are often employed. General formulae for the matrix elements of various operators can be found in the textbook. However the Fourier transform of correlated gaussians and their application to the management of a relativistic kinetic energy operator are missing and cannot be found in the literature. In this paper we present these interesting formulae. We give also a derivation for new formulations concerning central potentials; the corresponding formulae are more efficient numerically than those presented in the textbook.

Dates and versions

in2p3-00164650 , version 1 (23-07-2007)

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Cite

B. Silvestre-Brac, V. Mathieu. Few-body problem in terms of correlated gaussians. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2007, 75, pp.046702. ⟨10.1103/PhysRevE.76.046702⟩. ⟨in2p3-00164650⟩
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