Home /
Expert Answers /
Advanced Physics /
problem-4-the-three-dimensional-delta-function-perform-the-following-integrals-involving-the-three-pa284
(Solved): Problem 4: The Three-Dimensional Delta Function Perform the following integrals involving the three- ...
Problem 4: The Three-Dimensional Delta Function
Perform the following integrals involving the three-dimensional delta function:
(a) The position vector is vec(r) with magnitude r, and vec(a) is a constant vector with magnitude a.
\int_({(:[ all ]),( space ):}) d\tau (r^(2)-5(vec(r))*(vec(a))+2a^(2))\delta ^(3)(vec(r)-vec(a))
(b) The volume V is a cube centered on the origin with sides of length 9 , and vec(b)=7hat(x)-24hat(z)
\int_V d\tau |vec(b)-vec(r)|^(2)\delta ^(3)(10vec(r))