Recent content by naqo

Hi there, i have been studying a bit about QM, but ther's one fundamental question about the wavefunction i can't understand: why is the wavef. defined complex? I mean, couldn't one work from the beginning with a real wave? Thanks

aaaa sory about the symbols... just starting with latex...

Okay, in order to understand a little more about the number e, one must analyze first the limit presented above, \lim_{n\rightarrow \infty}(1+\frac{1}{n})^n. In particular, one must prove that such limit exists, that means, that when you take n really big, the number doesn't go to infinity. To...

Hi, i would proceed as follows: In the first case, one can easily see that the function f(n) is monotone decreasing and allways non-negative, so the integral test applies in this situation. Then, the series will converge only if the integral from 1 to infinity of x/(x^2+1) dx converges (sory...

\(1+frac{1}{n})^n

\(1+frac{1}{n})^n=sum_{n=0}^{\n}\frac{\n!}{\(n-k)!\k!}

there was supposed to be a 1 in the numerator of the second sum...

Hi, i suposse i would procceed in the following way: Note that due to the fact that cos(x) is always smaller or equal than 1, cos^2(x) has the same behavior. So, the sum that you are asking: \sum_{n=1}^{\infty}\frac{\cos^2n}{n\sqrt n} is smaller than \sum_{n=1}^{\infty}\frac{\1}{n\sqrt n}...