Constructing squeezed states of light with associated Hermite polynomials

Arbitrary-Order Hermite Generating Functions for Coherent and Squeezed States

For use in calculating higher-order coherentand squeezedstate quantities, we derive generalized generating functions for the Hermite polynomials. They are given by ∑∞ n=0 z Hjn+k(x)/(jn + k)!, for arbitrary integers j ≥ 1 and k ≥ 0. Along the way, the sums with the Hermite polynomials replaced by unity are also obtained. We also evaluate the action of the operators exp[a(d/dx)] on well-behaved ...

The combinatorics of associated Hermite polynomials

We develop a combinatorial model of the associated Hermite polynomials and their moments, and prove their orthogonality with a sign-reversing involution. We find combinatorial interpretations of the moments as complete matchings, connected complete matchings, oscillating tableaux, and rooted maps and show weight-preserving bijections between these objects. Several identities, linearization form...

On Hermite-hermite Matrix Polynomials

In this paper the definition of Hermite-Hermite matrix polynomials is introduced starting from the Hermite matrix polynomials. An explicit representation, a matrix recurrence relation for the Hermite-Hermite matrix polynomials are given and differential equations satisfied by them is presented. A new expansion of the matrix exponential for a wide class of matrices in terms of Hermite-Hermite ma...

Quadratic Hermite-Padé polynomials associated with the exponential function

Gazeau−Klauder squeezed states associated with solvable quantum systems

A formalism for the construction of some classes of Gazeau−Klauder squeezed states, corresponding to arbitrary solvable quantum systems with a known discrete spectrum, are introduced. As some physical applications, the proposed structure is applied to a few known quantum systems and then statistical properties as well as squeezing of the obtained squeezed states are studied. Finally, numerical ...