Analytic Coulomb matrix elements in the lowest Landau level in disk geometry
- 1 March 2002
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 43 (3) , 1664-1667
- https://doi.org/10.1063/1.1446244
Abstract
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 integrals of products of Laguerre polynomials is obtained.Keywords
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