Abstract
In this paper we study certain families of complex Hermite polynomials and construct deformed versions of them, using a GL(2,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.
Mathematics Subject Classification (2010). 42C05, 33C45, 33C50, 81S99
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© 2015 Springer International Publishing Switzerland
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Balogh, F., Shah, N.M., Ali, S.T. (2015). On Some Families of Complex Hermite Polynomials and their Applications to Physics. In: Bhattacharyya, T., Dritschel, M. (eds) Operator Algebras and Mathematical Physics. Operator Theory: Advances and Applications, vol 247. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-18182-0_9
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DOI: https://doi.org/10.1007/978-3-319-18182-0_9
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-18181-3
Online ISBN: 978-3-319-18182-0
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