Recent content by the_doors

ok we can write for first example:##\frac {\partial (g^{ca}g^{db}F_{cd}F_{ab})}{\partial g^{ef}}## = ##\frac{\partial g^{ca}}{\partial g^{ef}}g^{db}F_{cd}F_{ab}+\frac{\partial g^{db}}{\partial g^{ef}}g^{ca}F_{cd}F_{ab}+\frac{\partial F_{cd}}{\partial g^{ef}}g^{ca}g^{db}F_{ab}+\frac{\partial...

for example if ##N_{\mu}(x^\nu)## be unit time like dynamical four velocity, what's happening ? i don't know explicit form of ##N_{\mu}##.

Homework Statement for example: ##\frac{\partial(F^{ab}F_{ab})}{ \partial g^{ab}} ## where F_{ab} is electromagnetic tensor. or ##\frac{\partial N_{a}}{\partial g^{ab}}## where ##N_{a}(x^{b}) ## is a vector field. Homework EquationsThe Attempt at a Solution i saw people write ##F^{ab}F_{ab}##...

Homework Statement is this statement is true : ##\nabla_\mu \nabla_\nu \sqrt{g} \phi = \partial_\mu \sqrt{g} \partial_\nu \phi## Homework EquationsThe Attempt at a Solution well we know ##\nabla_\mu \sqrt{g} =0## so it moves back : ## \nabla_\mu \sqrt{g} \nabla_\nu \phi =\sqrt{g} \nabla_\mu...

now i will edit post with the entire action.

No, this is part of action which i have problem with that

Homework Statement i want to find the variation of this action with respect to ## g^{\mu\nu}## , where ##N_\mu(x^\nu)## is unit time like four velocity and ##\phi## is scalar field. ##I_{total}=I_{BD}+I_{N}## ## I_{BD}=\frac{1}{16\pi}\int dx^4\sqrt{g}\left\{\phi...

hello guys , i'm looking for approximation of trigonometric and hyperbolic functions for small and large argument, is it correct to say sin(x)=x and tg(x)=x and tgh(x)=x and cos(x) = 1 and cosh(x)=1 and coth(x)=1/x for small x what about large x ? what can we say about exponential function...

two particles can be on first energy level with up and down spin direction so the space wave function is symmetric and spin wave function is in singlet state . what is wrong with this ?

hello guys , in this problem from zettili quantum mechanics that i attach , i think something is wrong , first the problem said two particles with spin 1/2 but didn't mention that the system is in singlet state or triplet state , so if the system be in triplet state then our spatial wave...

the problem is exactly here, with permutation : s_z in s_y basis : s_x but with unitary transformation or rotating method s_z in s_y basis : s_y . i mean why we have 2 results ? at last which of the results are correct ?

so the solution is incorrect ?

but in this sulotion set i attached , he consider -pi/2 . and in the third method , we get s_x , so finally which is correct ? s_x or s_y ? Thank you

hello guys Suppose an electron is in the spin state alpha=(a,b). if s_y is measured, what is the probability of result h/2 ? s_y eigenvector for +h/2 is |y+>=1/sqrt(2) (1,i)) so the probabilty is (<y+|alpha>)^2 . but in the solution i attached , the solution is different ! I'm confused ...

in the second method we need -pi/2 ( pi/2 clockwise) ( sakurai chapter 1 problem 24 ) and in the third method : http://www.pa.msu.edu/~mmoore/851HW13_09Solutions.pdf , page 3.