Using the coherent state representation of Wigner operator and the technique of integration within an ordered product (IWOP) of operators, this paper derives the Wigner function for the Hermite polynomial state (HPS). The tomogram of the HPS is calculated with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics.

Chinese PhysicsAug 1, 20078 citations

arXiv:1305.2596 · Journal of Russian Laser Research

Hermite Polynomial Representation of the Spin States

Dmitry B. Lemeshevskiy, Vladimir I. Man’ko

Published Mar 1, 2013• 2 citations

arXiv HTML PDF

DOI: 10.1007/s10946-013-9340-0

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The Holstein-Primakoff representation for spin systems is used to derive expressions with solutions that are conjectured to be the zeros of Hermite polynomials

H_n(x)

n \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.