Asymptotic Equation for Zeros of Hermite Polynomials from the Holstein-Primakoff Representation
Mathematical Physics
2015-06-08 v3 Other Condensed Matter
math.MP
Abstract
The Holstein-Primakoff representation for spin systems is used to derive expressions with solutions that are conjectured to be the zeros of Hermite polynomials as . This establishes a correspondence between the zeros of the Hermite polynomials and the boundaries of the position basis of finite-dimensional Hilbert spaces.
Keywords
Cite
@article{arxiv.1506.00541,
title = {Asymptotic Equation for Zeros of Hermite Polynomials from the Holstein-Primakoff Representation},
author = {Lucas Kocia},
journal= {arXiv preprint arXiv:1506.00541},
year = {2015}
}
Comments
3 pages, 3 figures, version 3 (eqs 6 & 7 rewritten in a more concise form; typo in eqn 5 fixed; footnote 9 with ref. 6 added)