Homework Statement
We have
R_{iklm;n}+R_{iknl;m}+R_{ikmn;l} \equiv 0
Show that by multiplying above with g^{im}g^{kn}
we'll get
\left( R^{ik}-\frac{1}{2} g^{ik} R \right)_{;k}
2. The attempt at a solution
g^{im}g^{kn} \left( R_{iklm;n}+R_{iknl;m}+R_{ikmn;l} \right) \equiv 0...
Terribly sorry, I should've made my question clearer. All of the ps in my post refers 4-momenta while \vec{\textbf{p}} refers to 3 momenta.
I'm working in the CM frame.
In this scattering reaction the subscripts refers to the particle in the reaction as follows: 1 + 2 -> 3 + 4
@andrien, you...
Homework Statement
For a scattering problem A + A - > B + B in the Toy Theory,
Need to show
(p_4-p_2)^2-m_C^2c^2=p_4^2+p_2^2-2p_4\cdot p_2 = -\vec{\textbf{p}}^2(1-\cos\theta)Homework Equations
this is assuming m_A=m_B=m and m_C=0The Attempt at a Solution
p_4^2+p_2^2=2m^2c^2
but I'm not sure...
Here's what I have so far:
(B_{ij} B_{kl} + B_{il}B_{kj})A_{ik}\\
=B_{ij} B_{1l}A_{i1}+B_{ij}B_{2l}A_{i2}+B_{il} B_{1l}A_{i1}+B_{il}B_{2j}A_{i2}\\
=B_{1j} B_{1l}A_{11}+B_{2j} B_{1l}A_{21}+B_{1j}B_{2l}A_{12}+B_{2j}B_{2l}A_{22}+B_{1l} B_{1l}A_{11}+B_{2l}...
Homework Statement
If A_{ij} is a skew-symmetric tensor, and B_{ij} is a second-order tensor, evaluate the expression
(B_{ij} B_{kl} + B_{il}B_{kj})A_{ik}
and express the final answer in its simplest form.
Homework Equations
For a skew-symmetric tensor, A_{ik}=-A_{ki}
The...
Homework Statement
This is problem in Mandl's book on Stats Phys; The vapour pressure of water at 298.15 K is 23.75 mmHg. What is the vapour pressure of water at 273.16 K, given that the latent heat of evaporation of water at 298.15 and 273.16 K is 43,991 and 45,049 J/mol respectively?Homework...
Homework Statement
A ‘lattice gas’ consists of a lattice of N sites. Each of these sites can be empty, in which
case its energy is zero, or occupied by one particle, in which case its energy is e. Each particle
has a magnetic moment of magnitude μ which in the presence of an applied magnetic...
Amazing water trick?? Is this physically possible??
This vid has became viral recently.
So is this physically possible?! I am skeptical from the way the water behaves when it washes away from the cup's shape.
And the fact that the rest of the guy's uploaded videos are of animation stuff...
In the derivation of the relativistic kinetic energy,
K=\int_{x_1}^{x_2}F\,dx = \int_{0}^{v}\frac{d}{dt}(mv)\,dx = \int_{0}^{v}(mv\,dv+v^2\,dm)
here, my lecturer told us without showing that
mv\,dv+v^2\,dm = c^2\,dm
Can someone please give me hints on how to combine these two integrals? I...
Homework Statement
Hello. I am doing some problems on integration by parts and got stuck on the following problems. Any help would be appreciated.
i. \int \arcsin x dx
ii. \int_{0}^{1} x \ln (9+x^2) dx
iii. \int x^2 \arctan x\, dx
Homework Equations
u\,du=uv-v\,du
The Attempt at a...
After much thinking, I realized that i should have considered the forces acting on each body seperately.
Calling f the frictional force, we have acting on the block,
F-f=M_b a_b...(1)
Here Mb and ab are masses and acceleration of the block. f here is the frictional force acted by the can ON...