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Some Biorthogonal Families of Polynomials Arising in Noncommutative Quantum Mechanics (1309.4163v1)
Published 17 Sep 2013 in math-ph and math.MP
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.