Recent content by Muh. Fauzi M.

I think Greiner missprint the result. I've finally got the contraction result: $$ L_{\mu\nu}=8\Big(2(k\cdot p)(k'\dot p)+\frac{1}{2}q^2 M^2\Big) ,$$ and if I use the relativistic limit, my result is confirmed.

Homework Statement Proof the leptonic-hadronic tensor multiplication, with ##p^\mu=(M,\textbf{0})## and ##p'^\mu=(E',\textbf{p}')## is rest target and final target momentum respectively, and ##k^\mu=(\omega,\textbf{k})##, ##k'\mu=(\omega' ,\textbf{k}')## is momenta of incoming and outgoing...

update, I have finish this work.

Thanks for your clue. I am using Schwinger-Tomonaga equation, where the Hamiltonian that evolve with time is only the time dependent. CMIIW

I don't include the ## B_z \sigma_3 ## because it time independent. I realized that I don't differentiate with time the ##{B_1 cos (\omega t) \mp i B_2 sin (\omega t)}## term in the ##\partial a/\partial t## and ##\partial b/\partial t##. Here's my result after differentiating it (for ##...

The hydrogen is placed in the external magnetic field: $$ \textbf{B}=\hat{i}B_1 cos(\omega t) + \hat{j} B_2 sin(\omega t) + \hat{k} B_z ,$$ Using the relation ## H = - \frac{e\hbar}{2mc} \mathbf \sigma \cdot \mathbf B ##, then I got the form $$ H = H_0 + H' , $$ where $$ H'= - \frac{e...

ah, I've got it. solved by myself.

Homework Statement This is just a simple proof of substitution, but after one day struggle, I still can't get where that minus sign appear. Homework Equations Here is the equation: $$ (p_1 - p_3)^2=-(\mathbf p_1 - \mathbf p_3)^2$$ where ##p_1=(E/c,\mathbf p_1)## and ##p_3=(E/c, \mathbf p_3)##...

Speechless. That's true Mr. Thank you very much. (shy)

Hello Mr., thank you for your respond. In my first reference (Halzen and Martin), the instructor is to integrate over ##\theta## and ##\phi##. Here is my doodling: $$ \sigma = \frac{\alpha^2}{4s}\int{(1+cos^2{\theta})}d\theta d\phi $$ Substituting the trigonometry identity, $$ \sigma =...

Homework Statement I have a problem in calculating cross-section in elektron-positron -> muon-antimuon scattering. Homework Equations In the relativistic limit, we find the differential cross-section of {e}+{e^-} -> {μ}+{μ^-} is \frac{d\sigma}{d\Omega}=\frac{\alpha^2}{4s}*(1+cos^2{\theta})...

hello sir, i can't get the 3rd step. is change the integration variable, change the value from k to -k in that term, including the dk -> d(-k)?

I see mr. that's my problem actually. But for accomplishing an assignment in the short of time, I fall to just using a deductive reasoning. Well, let use your advice, so ##\sum_{r=0}^n T_{2r}(x)=\sum_{r=0}^n\cos(2r\theta)=1+\cos(2\theta)+\cos(4\theta)+...+\cos(2n\theta)## Then... Can't see the...

Thanks for your respond. I've made it by choosing an arbitrary ##n## and then evaluate both ##\sum_{r=0}^n T_{2r}(x)## and ##U_{2n+1}(x)##, for example ##n=1##, and, voila... :woot:

This is something Chebyshev polynomial problems. I need to show that: ##\sum_{r=0}^{n}T_{2r}(x)=\frac{1}{2}\big ( 1+\frac{U_{2n+1}(x)}{\sqrt{1-x^2}}\big )## by using two type of solution : ##T_n(x)=\cos(n \cos^{-1}x)## and ##U_n(x)=\sin(n \cos^{-1}x)## with ##x=\cos\theta##, I have form the...