论文信息 - Incomplete 2D Hermite polynomials: properties and applications

Incomplete 2D Hermite polynomials: properties and applications

Incomplete forms of two-variable two-index Hermite polynomials are introduced. Their link with Laguerre polynomials is discussed and it is shown that they are a useful tool to study quantum mechanical harmonic oscillator entangled states. The possibility of developing the theory of complete 2D Hermite polynomials from the point of view of the incomplete forms is analyzed too. The orthogonality properties of the associated harmonic-oscillator functions are finally discussed.

G. Dattoli

[1] MISCELLANEOUS IDENTITIES OF GENERALIZED HERMITE POLYNOMIALS , 1998 .

[2] Giuseppe Dattoli,et al. Theory and applications of generalized Bessel functions , 1996 .

[3] V. Man'ko,et al. New relations for two-dimensional Hermite polynomials , 1993, hep-th/9312012.

[4] C. Chiccoli,et al. Generalized Bessel Functions and Generalized Hermite Polynomials , 1993 .

[5] G. Dattoli. Laguerre and generalized hermite polynomials: the point of view of the operational method , 2004 .

[6] Giuseppe Dattoli,et al. An alternative point of view to the theory of fractional Fourier transform , 1998 .

[7] Phase‐space dynamics and Hermite polynomials of two variables and two indices , 1994 .

[8] Alfred Wünsche,et al. Laguerre 2D-functions and their application in quantum optics , 1998 .

[9] S. Lorenzutta,et al. Theory of multiindex multivariable Bessel functions and Hermite polynomials , 1998 .

[10] Alfred Wünsche,et al. Transformations of Laguerre 2D polynomials with applications to quasiprobabilities , 1999 .

[11] A. Turbiner,et al. Lie-algebraic discretization of differential equations , 1995, funct-an/9501001.