How To Without Green Function
For an nxn matrix A, G is its
inverse matirx if
A G = Id,
the identity matrix. e. ,t)) = \delta(. [2] D.
The solution for these four equations is A= (2t – 1)/4, B = -1/2,
C = -(2t + 1)/4, and D = 1/2.
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. 32} \end{equation}and the formal solution to Poisson’s equation,\begin{equation} V(\boldsymbol{r}) = \int G(\boldsymbol{r},\boldsymbol{r’}) f(\boldsymbol{r’})\, dV’.
Pick 0 t 1:
We have four constants to determine; here are four equations:
0 = G(0,t) + G(1,t) = A + C + D,
0 = Gx(0,t)) + Gx(1,t)) = B + D,
0 = G(t+,t) – G(t-,t) = (C – A) + (D – B) t,
1/a2(t) = Gx(t+,t) –
Gx(t-,t)) = D – B. G(x,y)∼L−1∼(dx2d2+x2)−1.
Here the specific position is
x
0
(
x
,
x
02
,
x
03
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)
{\displaystyle \mathbf {x_{0}} \equiv (x_{01},x_{02},x_{03})}
and the general coordinate position is
x
(
x
1
,
x
2
,
Homepage x
3
)
. .