Mathematics

  2010 AUG 31 - (VerticalNews.com) -- "In this paper we study the Arik-Coon oscillator with the main relation aa(+) - qa(+)a = 1, where q> 1, in the framework of the unified (q; alpha, beta, gamma; nu)-deformed oscillator algebra," investigators in Kiev, Ukraine report.

  "This oscillator is connected with the Askey q(-1)-Hermite polynomials. We construct a family of the generalized coherent states associated with these polynomials and give their explicit expression in terms of standard special functions," wrote I.M. Burban and colleagues ...read more

  2010 AUG 31 - (VerticalNews.com) -- "It is known that the anti-Wick (or standard coherent state) quantization of the complex plane produces both canonical commutation rule and quantum spectrum of the harmonic oscillator (up to the addition of a constant). In this work, we show that these two issues are not necessarily coupled: there exists a family of separable Hilbert spaces, including the usual Fock-Bargmann space, and in each element in this family there exists an overcomplete set of unit-norm states resolving the unity," investigators in Bucharest, Romania report ...read more

  2010 AUG 31 - (VerticalNews.com) -- According to recent research published in the Journal of Physics a - Mathematical and Theoretical, "The information-theoretic lengths of the Jacobi polynomials P-n((alpha,beta)) (x), which are information-theoretic measures (Renyi, Shannon and Fisher) of their associated Rakhmanov probability density, are investigated. They quantify the spreading of the polynomials along the orthogonality interval [-1, 1] in a complementary but different way as the root-mean-square or standard deviation because, contrary to this measure, they do not refer to any specific point of the interval. ...read more