Some Biorthogonal Families of Polynomials Arising in Noncommutative Quantum Mechanics

Abstract

In this paper we study families of complex Hermite polynomials and construct deformed versions of them, using a $GL(2,\mathbb{C})$ transformation. This construction leads to the emergence of biorthogonal families of deformed complex Hermite polynomials, which we then study in the context of a two-dimensional model of noncommutative quantum mechanics.

17 pages

References in corpus (3)

• A class of generalized complex Hermite polynomials
• Harmonic oscillator in a background magnetic field in noncommutative quantum phase-space
• A new kind of representations on noncommutative phase space

Cited by in corpus (1)

• $\mathcal{D}$-Pseudo-Bosons, Complex Hermite Polynomials, and Integral Quantization