Jan 19, 2020
If I never see a Bessel function again, I’d be happy
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If I never see a Bessel function again, I’d be happy
Tangents
(source code)
Bessel
(source code)
Derivation of the 2D Green's function for the wave equation operator.
[Click here for a PDF version of this post] While it was difficult to attempt to verify the 2D Green’s function, it actually turns out to be fairly easy to derive it, provided we pick an alternate pole displacement from the 1D evaluation to make our lives easier. With \( \Br = \Bx – \Bx’ \), and \( \tau = t – t’ \), and \( \epsilon > 0 \), we can…
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A trilogy in four+ parts: The 2D Laplacian Green's function.
[Click here for a PDF version of this post] I was questioning the correctness of the 1D and 2D Helmholtz Green’s functions derived above, since they are both seemingly malformed for \( k \rightarrow 0 \). Let’s try to carefully expand the 2D Green’s function in the neighbourhood of \( k = 0 \) to validate that result, and as a side effect, obtain the Green’s function for the 2D Laplacian. In [1],…
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Read the full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=49617 DOI: 10.4236/am.2014.516249 Author(s) Mohamed Vall Ould Moustapha Affiliation(s) Unité de Recherche: Analyse, EDP et Modélisation (AEDPM), Département de Mathématiques et Informatique, Faculté des Sciences et Techniques, Universitè des Sciences, de Technologie et de la Médecine (USTM), Nouakchott, Mauritanie. ABSTRACT In this paper, the heat, resolvent and wave kernels associated to the Schr?dinger operator with multi-inverse square potential on the Euclidian space Rn are given in explicit forms.gjreww140916 KEYWORDS Heat Kernel, Wave Kernel, Resolvent Kernel, Multiple-Inverse Square Potential, Bessel Function, Lauricella Hypergeometric Function
Okay, I think I'm done with this subpixel business. Maybe I'll do a gif.
using a Bessel function to find the energy in an atom if initial state is given as a partial differential equation... it's a nuclear Bessel i'm going to fail my class