The Functions of Mathematical Physics by Harry Hochstadt

Author:Harry Hochstadt [Hochstadt, Harry]
Language: eng
Format: epub
Tags: Mathematics, Science, Calculus, Functions; Special, Mathematical Physics
ISBN: 9780471401704
Publisher: Dover Publications
Published: 1971-01-15T06:22:25+00:00

where δ(P, P0) is a delta function. Here P and P0 denote two points in space P = (r, θ, φ), P0 = (r0, θ0, φ0). P0 will be taken as a fixed point. The function δ(P, P0) is so constituted that

but

where the above is a volume integral over any simple connected domain D having P0 as an interior point. Physically G can be interpreted as the potential inside the sphere due to a point charge at P0 with a perfectly conducting surface constituting the boundary of the sphere.

Using Green's theorem we have immediately

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