:Also, wave particle duality tells us that things we think of as particles are actually " wave packets ", with a location described by a " probability function ".
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You mentioned wave-functions, so do you intend to show that the integral of e ^-| x | is integrable and that the probability function integrates to 1?
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The simplest way to think of electrons is as spherical particles, but a more correct way to think of them is as quanta of energy with a probability function describing their position.
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The total current for a many-state system is then the sum over the energy of each state multiplied by the occupation probability function, in this case the Fermi Dirac statistics:
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However, the Hirschman entropic uncertainty will have a useful analog for the case of the DFT . The Hirschman uncertainty principle is expressed in terms of the Shannon entropy of the two probability functions.
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These belong to the categories basic functions, trigonometric and hyperbolic functions, non-differentiable functions, probability functions, special functions, programmable functions, iterations and fractals, differential and integral equations.
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In quantum mechanics, it doesn't really behave much like a particle at all, but more like a wave, which only has a probability function, not a location and volume.
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The probability of finding, within a particle, a point i at a distance r from a given point j is given by the distance probability function \ gamma _ 0 ( r ).
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The surface roughness model used in the derivation of the Oren-Nayar model is the microfacet model, proposed by roughness of the surface is specified using a probability function for the distribution of facet slopes.
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The authors Kemp and Kemp have called it " Hermite distribution " from the fact its probability function and the moment generating function can be expressed in terms of the coefficients of ( modified ) Hermite polynomials.
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