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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 Hn(x)H_n(x) as nn \rightarrow \infty. 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)