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Article overview
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Tan's distributions and Fermi-Huang pseudopotential in momentum space | Manuel Valiente
; | Date: |
1 Sep 2011 | Abstract: | The long-standing question of finding the momentum representation for the
s-wave zero-range interaction in three spatial dimensions is here solved. This
is done by expressing a certain distribution, introduced in a formal way by S.
Tan [Ann. Phys. 323, 2952 (2008)], explicitly. The resulting form of the
Fourier-transformed pseudopotential remains very simple. Operator forms for the
so-called Tan’s selectors which, together with Fermi-Huang pseudopotential,
largely simplify the derivation of Tan’s universal relations for the Fermi gas,
are here derived and are also very simple. A momentum cut-off version of the
pseudopotential is also provided, and with this no apparent contradiction with
the notion of integrals in Tan’s methods is left. The equivalence, even at the
intermediate step level, between the pseudopotential approach and
momentum-space renormalization of the bare Dirac delta interaction is then
shown by using the explicit form of the cut-off pseudopotential. | Source: | arXiv, 1109.0145 | Services: | Forum | Review | PDF | Favorites |
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