The potential of the hydrogenatom is given by:
$\phi(r) = \frac{1}{4 \pi \epsilon_0} \frac{e}{r} ( 1 + \frac{r}{a_0}) e^{-\frac{2r}{a_0}}$
I'm no supposed to find the volume charge density $\psi$ which produces such a potential, which conceptually is fairly simple, just slap on the Laplacian fr...
Put another way : let f be continu at (0,2) apart from a discontinu point at 1. If f is constant at (0,1( how to prove (IN a case where it is true) that f(1) is the same value as f(0) ?
In other words , when I know there is discontinu point , i want to know the output value
@BenjaLim Since U is the kernel of tr:K[G]->K, in order for K[G]=U(+)V we must have V iso to K as a G-module, which means V must be generated by a G-invariant element of K[G], and such a thing has equal coefficients hence trace zero hence is in U, contrary to the assumption of directness of the decomposition of K[G] into U and V.
@anon I understand the question is general , but I would like some quite general techniques to solve such questions. That is assuming you understand what I said or maybe better stated : Assuming I made myself clear.
Lets say f( [0,1[ ) => A and f( ]1,2] ) => A where A is a connected set (curve on the complex plane) . How do I FIND f(1) when f is given ?? ( f is the inverse of an analytic function ) @robjohn
$f$ is locally Lipschitz in $y$ if for every $(t_0, y_0) \in (c,d) \times U$, there exists a neighborhood V of $(t_0, y_0)$, (i.e. $V = \{f(t,y) \in(c,d) \times U : ||t-t_0|<a \ \text{and} \ |y-y_0|\leq b\}$) and a constant K = K(V) such that $||f(t,x)-f(t,y)||\leq K||x-y||$
for any $(t,x),(t,...
@mick Oh, that is why I asked about the continuity. If it is discontinuous, then I don't see how you can find the value. With Fourier Series, the convergence at a discontinuity is the average of the limits from either side.
I am stuck on the following problem:
Suppose an entire function maps two horizontal lines onto two other horizontal lines. Prove that its derivative is periodic.
The author supplies a hint: Assume $f = u+iv$ maps the lines $y=y_1$ and $y=y_2$ onto $v=v_1$ and $v=v_2$ with $y_2-y_1 = c$ and ...
The potential of the hydrogenatom is given by:
$\phi(r) = \frac{1}{4 \pi \epsilon_0} \frac{e}{r} ( 1 + \frac{r}{a_0}) e^{-\frac{2r}{a_0}}$
I'm no supposed to find the volume charge density $\psi$ which produces such a potential, which conceptually is fairly simple, just slap on the Laplacian fr...
$f$ is locally Lipschitz in $y$ if for every $(t_0, y_0) \in (c,d) \times U$, there exists a neighborhood V of $(t_0, y_0)$, (i.e. $V = \{f(t,y) \in(c,d) \times U : ||t-t_0|<a \ \text{and} \ |y-y_0|\leq b\}$) and a constant K = K(V) such that $||f(t,x)-f(t,y)||\leq K||x-y||$
for any $(t,x),(t,...
I am stuck on the following problem:
Suppose an entire function maps two horizontal lines onto two other horizontal lines. Prove that its derivative is periodic.
The author supplies a hint: Assume $f = u+iv$ maps the lines $y=y_1$ and $y=y_2$ onto $v=v_1$ and $v=v_2$ with $y_2-y_1 = c$ and ...
