Recent content by HotMintea

I meant E[S_n^2] = . I found the proof of E[X]E[Y] = E[XY] , if X and Y are random variables, which basically uses P(X,Y) = P(X)P(Y). \hspace{2 cm} http://webpages.dcu.ie/~applebyj/ms207/RV2.pdf" So now I get that Var[S_n] = n\sigma^2 . Thanks for the help :smile:

Homework Statement Suppose X1 , X2 , . . . , Xn are independent random variables, with common expectation μ and variance σ^2 . Let Sn = X1 + X2 + · · · + Xn . Find the variance of Sn. The attempt at a solution Expected value: E[S_n] = n E[X_i] = n\mu \hspace{10 cm} (1)...

These are tutorials on differential forms applied to Thermo. I like them because they are highly visual: http://www.av8n.com/physics/thermo-forms.htm http://www.av8n.com/physics/partial-derivative.htm There's also an online Thermo book written by the same author. The author has a lot to say...

Hi, How were the books ?:confused:

I'd like to know how to do it without solving via Hermite polynomials, so that I can check by both methods when I solve other problems. I have tried to figure out myself but I need some help. Let's say H:=x^2+p^2 , and a:= x-ip . So that [a,a^+]=2\hbar , H a \varphi_i = (E_i -...

Thanks for the explanation. Now I understand why. It definitely worked. I tried out the mailing list archive. It seems great. I'll try them when the archive doesn't work. Thank you very much for your informative answer.:smile:

Okay, I'll be more specific. Basically, I'd like to give names to the derivatives of functions. The following is how I tried.A(x):=A1*exp(%i*k*x)+A2*exp(-%i*k*x); Ax(x):=diff(A(x), x,1); B(x):=A2*exp(-%i*k*x); Bx(x):=diff(B(x),x,1); C(x):=C1*exp(j*x)+C2*exp(-j*x); Cx(x):=diff(C(x),x,1)...

For example, F(x) := x^2; Fx(x) := diff(F(x),x,1); didn't seem to work, since Fx(3); returned an error. Any help would be appreciated.

Thanks for the hints! \frac{d}{dt}\partial_{x}f(x(t), y(t), t)=(\sum\dot{x}_k \partial_{x_k}+\partial_t)\partial_{x}f=\sum\dot x_k\partial_{x_k}\partial_{x}f+\partial_t\partial_{x}f . At this point, I need to show the "equality of mixed partials". I found the proof of f_{xy}=f_{yx} for...

Problem I'd like to prove \frac{d}{dt}[\frac{\partial}{\partial{x}}f(x(t),y(t),t)]=\frac{\partial}{\partial{x}}[\frac{d}{dt}f(x(t),y(t),t)]. Attempt \begin{equation*}\begin{split} \frac{d}{dt}[\frac{\partial}{\partial x}f(x(t),y(t),t)]=\frac{d}{dt}\lim_{\epsilon\to...

Thanks for your help!:smile: I also liked the article you referred to.

Could someone explain what the 'first order' diffraction peak is?

23*5*10^-7m / 2*0.02m = 0.0002875 It agrees ↓ Air at STP | 1.000277 Air (0 C and 1 atm) | 1.000293 (http://en.wikipedia.org/wiki/List_of_refractive_indices#List)

Since wavelength gets longer as the air gets thinner, I think the number of wavelengths in the distance 2d will decrease as the air gets pumped out. The index of refraction in vacuum is defined to be 1. I have: m λ/n = (m - 23) λ/1 = 2d. The left side says integer m times the contracted...

Homework Statement A Fabry-Perot interferometer has spacing d = 2 cm between the glass plates, causing the direct and doubly reflected beams to interfere. As air is pumped out of the gap between the plates, the beams go through 23 cycles of constructive-destructive-constructive interference...