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Non-local separable solutions of two interacting particles in a harmonic trap

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Publication Date
2011-01-17
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González-Santander de la Cruz, Clara
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Elsevier
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Abstract
We calculate the energy levels of two particles trapped in a harmonic potential. The actual two-body potential, assumed to be spherically symmetric, is replaced by a projective operator (non-local separable potential) to determine the energy levels in a closed form. This approach overcomes the limitations of the regularized Fermi pseudopotential when the characteristic length of the two-body interaction potential is of the order of the size of the harmonic trap. In addition, we recover the results obtained with the Fermi pseudopotential when the length of the interaction is much smaller than the size of the trap.
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©2010 Elsevier B.V. All rights reserved. The authors thank J. M. R. Parrondo for discussions. This work was supported by MICINN (projects Mosaico and MAT2010-17180). C. G.-S. acknowledges financial support from Comunidad de Madrid and European Social Foundation.
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