- #1
Pushoam
- 962
- 51
Homework Statement
Calculate
##\int_{r=0}^\inf δ_r (r -r_0)\,dr##
Homework Equations
##\int_V \delta^3(\vec{r} - \vec{r}') d\tau = 1##
The Attempt at a Solution
$$\int_V \delta^3(\vec{r} - \vec{r}') d\tau =
\int_V \frac {1}{r^2 sinθ}\delta_r(r-r_0) \delta_θ (θ-θ_0) \delta_Φ (Φ-Φ_0) r^2 sinθ dr dθ dΦ = 1
$$
$$\int_{r=0}^ \inf \delta_r(r-r_0) dr \int_{θ=0}^{π/2}\delta_θ (θ-θ_0) dθ\int_{Φ=0}^{2π}\delta_Φ (Φ-Φ_0) dΦ = 1$$
$$\int_{r=0}^ \inf \delta_r(r-r_0) dr = \int_{θ=0}^{π/2}\delta_θ (θ-θ_0) dθ = \int_{Φ=0}^{2π}\delta_Φ (Φ-Φ_0) dΦ = 1$$
Is this correct?