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Search Results: 1 - 10 of 189830 matches for " G. Dattoli "
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The truncated exponential polynomials, the associated Hermite forms and applications
G. Dattoli,M. Migliorati
International Journal of Mathematics and Mathematical Sciences , 2006, DOI: 10.1155/ijmms/2006/98175
Abstract: We discuss the properties of the truncated exponential polynomials anddevelop the theory of new form of Hermite polynomials, which can beconstructed using the truncated exponential as a generating function. Wederive their explicit forms and comment on their usefulness in applications,with particular reference to the theory of flattened beams, used in optics.
Special polynomials and elliptic integrals
D. Babusci,G. Dattoli
Physics , 2009,
Abstract: We show that the use of generalized multivariable forms of Hermite polynomials provide an useful tool for the evaluation of families of elliptic type integrals often encountered in electrostatic and electrodynamics
The Dirac factorization method and the harmonic oscillator
D. Babusci,G. Dattoli
Physics , 2012,
Abstract: We apply the Dirac factorization method to the nonrelativistic harmonic oscillator and, more in general, to Hamiltonians with a generic potential. It is shown that this procedure naturally leads to a supersymmetric formulation of the problems under study. It is also speculated on the physical meaning underlying this method and it is suggested that the vacuum field fluctuations can be viewed as the spontaneous emission of the associated two-level system, whose quantization is due to the noncommuting nature of the harmonic oscillator canonical variables.
A Note on Coriolis Quantum States
G. Dattoli,M. Quattromini
Physics , 2010,
Abstract: We introduce the Coriolis quantum states in analogy to the Landau states. We discuss their physical meaning and their role within the context of gravito-magnetic theory. We also analyse the experimental conditions under which they can be observed and their link with the Aharanov-Carmi effect.
Heat Polynomials, Umbral Correspondence and Burgers Equations
G. Dattoli,D. Levi
Physics , 2006,
Abstract: We show that the umbral correspondence between differential equations can be achieved by means of a suitable transformation preserving the algebraic structure of the problems. We present the general properties of these transformations, derive explicit examples and discuss them in the case of the App\`{e}l and Sheffer polynomial families. We apply these transformations to non-linear equations, and discuss how the relevant solutions should be interpreted.
On Ramanujan Master Theorem
D. Babusci,G. Dattoli
Physics , 2011,
Abstract: In this short note we use the umbral formalism to derive the Ramanujan Master Theorem and discuss its extension to more general cases.
Bunching coefficients in Echo-Enabled Harmonic Generation
G. Dattoli,E. Sabia
Physics , 2013,
Abstract: Coulombian diffusion determines a dilution of bunching coefficients in Free Electron Laser seeded devices. From the mathematical point of view the effect can be modeled through a heat type equation, which can be merged with the ordinary Liouville equation, ruling the evolution of the longitudinal phase space beam distribution. We will show that the use of analytical tools like the Generalized Bessel Functions and algebraic techniques for the solution of evolution problems may provide a useful method of analysis and shine further light on the physical aspects of the underlying mechanisms.
Generalized Transforms and Special Functions
G. Dattoli,E. Sabia
Physics , 2010,
Abstract: We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A general method, based on the use of the Fourier transform technique, is proposed for the study of the properties of functions of operators.
Linear Potentials, Airy Wave Packets and Airy Transform
G. Dattoli,K. Zhukovsky
Physics , 2010,
Abstract: The solution of the Schrodinger equation with a linear potential is considered. We use algebraic methods to obtain the explicit form of the solution for the explicitly time dependent Hamiltonian and discuss the general conditions which allow us to get solutions in terms of the Airy functions, yelding non spreading wave packets. We analyze the relevant physical meaning of these solutions and give examples of their applications. We discuss the analogy between Airy and Gauss-Weirestrass transform.
Umbral methods and operator ordering
D. Babusci,G. Dattoli
Physics , 2011,
Abstract: By using methods of umbral nature, we discuss new rules concerning the operator ordering. We apply the technique of formal power series to take advantage from the wealth of properties of the exponential operators. The usefulness of the obtained results in quantum field theory is discussed.
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