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)

    “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)

    “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)

    “Jail sentences have many functions, but one is surely to send a message about what our society abhors and what it values. This week, the equation was twofold: female infidelity twice as bad as male abuse, the life of a woman half as valuable as that of a man. The killing of the woman taken in adultery has a long history and survives today in many cultures. One of those is our own.”
    —Anna Quindlen (b. 1952)