Screened Poisson Equation - Statement of The Equation

Statement of The Equation


\left u(\mathbf{r}) = - f(\mathbf{r})

Where is the Laplace operator, λ is a constant, f is an arbitrary function of position (known as the "source function") and u is the function to be determined.

In the homogenous case (f=0), the screened Poisson equation is the same as the time-independent Klein–Gordon equation. In the inhomogeneous case, the screened Poisson equation is very similar to the inhomogeneous Helmholtz equation, the only difference being the sign within the brackets.

Read more about this topic:  Screened Poisson Equation

Famous quotes containing the words statement of the, statement of, statement and/or equation:

    It is commonplace that a problem stated is well on its way to solution, for statement of the nature of a problem signifies that the underlying quality is being transformed into determinate distinctions of terms and relations or has become an object of articulate thought.
    John Dewey (1859–1952)

    It is commonplace that a problem stated is well on its way to solution, for statement of the nature of a problem signifies that the underlying quality is being transformed into determinate distinctions of terms and relations or has become an object of articulate thought.
    John Dewey (1859–1952)

    Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth.
    Charles Sanders Peirce (1839–1914)

    A nation fights well in proportion to the amount of men and materials it has. And the other equation is that the individual soldier in that army is a more effective soldier the poorer his standard of living has been in the past.
    Norman Mailer (b. 1923)