• Corpus ID: 118238781

On the Laplacian of 1/r

@article{Redi2013OnTL,
  title={On the Laplacian of 1/r},
  author={D V Red{\vz}i{\'c}},
  journal={arXiv: General Physics},
  year={2013}
}
  • D. Redžić
  • Published 8 March 2013
  • Mathematics
  • arXiv: General Physics
A novel definition of the Laplacian of 1/r is presented, suitable for advanced undergraduates. 

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Generalized second-order partial derivatives of 1/r

The generalized second-order partial derivatives of 1/r, where r is the radial distance in three dimensions (3D), are obtained using a result of the potential theory of classical analysis. Some

Some novel delta‐function identities

Two novel identities arising from the second‐ and thirdorder derivatives of the reciprocal radial distance and involving delta functions are introduced, proven, and illustrated. A general procedure

Delta functions in spherical coordinates and how to avoid losing them: Fields of point charges and dipoles

In calculations involving the divergence, curl, or Laplacian operators in spherical polar coordinates, the radial delta function contributions are sometimes inadvertently lost. This loss can be

Time-dependent fields of a current-carrying wire

The electric and magnetic fields of an infinite straight wire carrying a steady current which is turned on abruptly are determined using Jefimenko's equations, starting from the standard assumption

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The operator ? in orthogonal curvilinear coordinates

It is possible to define a single expression for the operator ? in orthogonal curvilinear coordinates that can fit all common differential operators and vectorial identities.

On the Laplacian of 1/r

It is pointed out that the distinction between `standard' and `non-standard' representations of the radial delta function (r) emphasized by Menon in a recent paper on the solving of the radial