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:

    Eroticism has its own moral justification because it says that pleasure is enough for me; it is a statement of the individual’s sovereignty.
    Mario Vargas Llosa (b. 1936)

    Most personal correspondence of today consists of letters the first half of which are given over to an indexed statement of why the writer hasn’t written before, followed by one paragraph of small talk, with the remainder devoted to reasons why it is imperative that the letter be brought to a close.
    Robert Benchley (1889–1945)

    If we do take statements to be the primary bearers of truth, there seems to be a very simple answer to the question, what is it for them to be true: for a statement to be true is for things to be as they are stated to be.
    —J.L. (John Langshaw)

    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)