Analytic Coulomb matrix elements in the lowest Landau level in disk geometry

Details Analytic Coulomb matrix elements in the lowest Landau level in disk geometry Analytic Coulomb matrix elements in the lowest Landau level in disk geometry

2001-11-27

arxiv.org/abs/cond-mat/0111516v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Accepted to J. Math. Phys.; 3 pages revtex, no figures

Scientific paper

Using Darling's theorem on products of generalized hypergeometric series an analytic expression is obtained for the Coulomb matrix elements in the lowest Landau level in the representation of angular momentum. The result is important in the studies of Fractional Quantum Hall effect (FQHE) in disk geometry. Matrix elements are expressed as simple finite sums of positive terms, eliminating the need to approximate these quantities with slowly-convergent series. As a by-product, an analytic representation for certain integals of products of Laguerre polynomials is obtained.

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