The evolution of piecewise polynomial wave functions
TLDR
In this article, the evolution of wave functions that consist of polynomial segments, usually joined smoothly together, is considered for a non-relativistic particle and its evolution can be expressed in terms of antiderivatives of the propagator.Abstract:
For a non-relativistic particle, we consider the evolution of wave functions that consist of polynomial segments, usually joined smoothly together. These spline wave functions are compact (that is, they are initially zero outside a finite region), but they immediately extend over all available space as they evolve. The simplest splines are the square and triangular wave functions in one dimension, but very complicated splines have been used in physics. In general the evolution of such spline wave functions can be expressed in terms of antiderivatives of the propagator; in the case of a free particle or an oscillator, all the evolutions are expressed exactly in terms of Fresnel integrals. Some extensions of these methods to two and three dimensions are discussed.read more
Citations
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Modeling the dynamics of hepatitis E via the Caputo–Fabrizio derivative
TL;DR: In this paper, the authors explored the HEV dynamics in fractional derivative and applied fixed point theory to obtain the existence and uniqueness results associated to the model by using Adams-Bashfirth numerical scheme.
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Enhancement of heat transfer in a convergent/divergent channel by using carbon nanotubes in the presence of a Darcy–Forchheimer medium
TL;DR: In this paper, the influence of thermal radiation on the flow and heat transfer of single-walled carbon nanotubes over both a convergent and divergent channel was explored.
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Small scale effects on buckling and postbuckling behaviors of axially loaded FGM nanoshells based on nonlocal strain gradient elasticity theory
TL;DR: In this article, a nonlocal strain gradient continuum theory is proposed to take small scale effects into consideration in a more accurate way, a non-local stress field parameter and an internal length scale parameter are incorporated simultaneously into an exponential shear deformation shell theory.
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A novel approach for investigation of heat transfer enhancement with ferromagnetic hybrid nanofluid by considering solar radiation
K. Ganesh Kumar,Ehab Hussein Bani Hani,Mamdouh El Haj Assad,Mohammad Rahimi-Gorji,Sohail Nadeem +4 more
TL;DR: In this article, the authors studied the stability analysis of heat transfer enhancement occurring due to the influence of significant properties variation of fluids in the presence of thermal radiation with the aid of suspended hybrid nanofluids.
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Non-Differentiable Exact Solutions for the Nonlinear ODEs Defined on Fractal Sets
TL;DR: In this paper, a family of special functions via the celebrated Mittag-Leffler function defined on the Cantor sets is investigated and the exact solutions for these problems are also discussed with the aid of the non-differentiable charts on Cantor sets.
References
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Book
An Introduction to Fourier Analysis and Generalised Functions
TL;DR: In this paper, the authors present a monograph on generalised functions, Fourier integrals and Fourier series, intended for readers who, while accepting that a theory where each point is proved is better than one based on conjecture, nevertheless seek a treatment as elementary and free from complications as possible.
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Applications of B-splines in atomic and molecular physics
TL;DR: In this article, the main properties of B-spline basis sets and why they are useful to solve different problems in atomic and molecular physics are discussed and an extensive reference list of theoretical works that have made use of them up to 2000 is provided.
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Diffraction in time
TL;DR: In this paper, the shutter problem is discussed for particles whose wave functions satisfy the Schr\"odinger equation, the ordinary wave equation, and the Klein-Gordon equation and the transient effects that appear when a shutter is opened are discussed.
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