Homework Statement
(a) Calculate the Conserved currents $$K_{\mu \nu \alpha} $$ associated with the global lorentz transformation and express them in terms of energy momentum tensor.
(b) Evaluate the currents for $$L=\frac{1}{2}\phi (\Box +m^2)\phi$$. Check that these currents satisfy...
After much thinking I have found that we need to use the equation for tidal forces acting on the spaceship as it approaches the star. and it appears that there is a big difference (a few hundred g's if i remember correctly) in gravitational acceleration between tip of the spaceship and its tail...
this is a small part of a problem on tidal forces and I wasn't sure what the question asks as it seems to me that more information is needed. Am I right or is there something im missing? the question goes as:
"A spacecraft approaches a neutron star of radius 10 km and mass 1.5 times mass of...
Homework Statement
A cylinder of permeability ##\mu## is placed in an external field ##B_0##. find the strength and direction of magnetic field inside the cylinder for:
a) when axis of cylinder is parallel to external field.
b) when axis of cylinder makes an angle ##\theta _0## with external...
I actually couldn't figure out how to edit the question and insert more details into it so I just created another thread at: "https://www.physicsforums.com/threads/canonical-transformation-two-degrees-of-freedom.846585/#post-5309162" and I included my attempt at solution there (I have actually...
so using the Hamiltonian equations of motion I have: $$\dot{Q_1}=\frac{\partial H}{\partial P_1}=aP_1 \Longrightarrow \frac{d(q_1^2)}{dt}=2q_1\dot{q_1}=aP_1\\\dot{Q_2}=\frac{\partial H}{\partial P_2}=b \Longrightarrow \dot{q_1}+\dot{q_2}=b\\\dot{P_1}=0\\\dot{P_2}=0$$ So I guess these are the...
Homework Statement
Point transformation in a system with 2 degrees of freedom is: $$Q_1=q_1^2\\Q_2=q_q+q_2$$
a) find the most general $P_1$ and $P_2$ such that overall transformation is canonical
b) Show that for some $P_1$ and $P_2$ the hamiltonain...
Homework Statement
If in a system with i degrees of freedom the $$Q_i$$ are given what is the best way to proceed for finding the $$P_i$$ so that we have an overall canonical transformation. say for a two degree freedom system we have $$Q_1=q_1^2 $$ and $$ Q_2=q_1+q_2$$
Homework Equations...
Thank you so much I have found it. it will be as following:
the four momentum of system after the collision and creation of two identical particle will be:
$$p^{\mu}_T=(2 \gamma mc,0,0,0)$$
now using $$\gamma=1$$ and using the invariance of the square of the total momentum in a reaction we get...
Homework Statement
Two photon of energy ##E_1 ## and ## E_2## collide with their trajectory at an angle $\theta$ with respect to each other.
a) Total four-momentum before collision?
b) square length of 4-momentum in lab frame (LB)and in center of momentum frame (CM)?
c) 4-momentum of two photon...
Homework Statement
A potential satisfies ##\nabla^2 Φ = 0## in the 2d slab ## -\inf < x < \inf ##, ##-b < y < b ##, with boundary conditions ## Φ(x, +b) = +V_s(x)## on the top and ##Φ(x, b) = -V_s(x)## on the bottom, where[/B]
##V_s (x)= -V_0 for -a<x<0##
##V_s (x)=+V_0 for 0<x<a##
(a) what...
since the problems says for every state A so should I write as following ##<A_i|L|A_i>=0 \to ## then as before
## <B_j|L|A_i>=\sum_{i}<B_j|A_i><A_i|L|A_i>=0##
is it right now?
Homework Statement
Suppose a linear operator L satisfies <A|L|A> = 0 for every state A. Show that then all matrix elements <B|L|A> = 0, and hence L = 0.
Homework Equations
##<A|L|A>=L_{AA} and <B|L|A>=L_{BA}##
The Attempt at a Solution
It seems very straight forward and I don't know how...
Homework Statement
A potential ##\phi(\rho, \phi ,z)## satisfies ##\nabla^2 \phi=0## in the volume ##V={z\geqslant a}## with boundary condition ##\partial \phi / \partial n =F_{s}(\rho, \phi)## on the surface ##S={z=0}##.
a) write the Neumann Green's function ##G_N (x,x')## within V in...
never mind I have found out where I was missing. your hint was very helpful. but there is one further question that pops out here. say we have written the greens function for such a problem in cylindrical coordinates, on the surface and considering the ##F_s = E_0## a constant, we arrive at the...
Lets say we have the following conditions given and we want to find the greens function in cylindrical coordinates:
## \nabla^2 \phi =0## this will eliminate the volume charge term in the equation for ##\phi##
we also have that ##\phi|_{s} = F_{s}(\rho , \phi)## at the surface...
I can't think of a situation where we can utilize greens function without the presence of a point charge. lets consider the following equation:
\Phi=\frac{1}{4\pi \epsilon} \int dv \rho(x')G_{N} (x,x')+ \frac{1}{4\pi} \int da F_{s}(\rho , \phi) G_{N} + <\phi>_S
Here we see that a volume...
first of all id like to thank you for taking time to answer my question. I have attached the 1st page of the original paper. well here we are dealing with lnZ since, later to find the average energy we have to take partial derivative of lnZ with respect to β.
in the paper written by Jose Torres-Hernandez in 1984 titled as : "Photon mass and blackbody radiation" in the first page he writes for the partition function:
lnZ=λ \sum_{normal modes} e^{-βε_l} = \frac{-λπ}{2} \int_{ε_0}^∞ n^2 ln(1-e^{-βε}) \frac{dn}{dε}dε
i really don't understand...
It is indeed odd. But even more surprisingly i found what it refers to after reading the next chapter.
After some pages it is indicated that the constant sigma actually refers to the damping constant (as the system is considered as damped oscillator since it emits radiation) but still i don't...
Thank you very much for your time.
actually that is the part i didn't understand. because i don't see any relation between the formula for the conseravation of energy and σ , in the book it just appears suddenly and then the author concludes the final equation (the differential equation) by...
consider energy for a damped electric oscillator . ("f" indicates the dipole moment of the oscillator)
in the absence of the damping force
U= \frac{1}{2}kx^2 +1/2 (\frac{d^2x}{dt^2}) ^2
and the energy conservation tells us dU=0.
but if there is damping force we get the following...
@naturale
and by the way naturale can you please show me the steps how you get that?
we put the solution into
ψ=Z(z)T(t)
get the follwoing:
ψ(z,t)=(Ae^{iωt} + Be^{-iωt})(Ce^{ikz} + De^{-ikz})
how do we apply the periodic conditions to this??
@Fredrik
well Im sorry I'm not really that good with -Latex- since i have just started using it.
for the momentum Im just applying the following formula:
π_μ = \frac{∂L}{∂(∂_μψ)}
and applying this to lagrangian
L=(1/2)[(∂ψ/∂t)^2 -(∂ψ/∂z)^2 -m^2ψ^2]
we get the follwing :
π_0 =...
@Fredrik
what I mean is that we have two partial derivatives (with respect to t,z) present in the Lagrangian so we have to apply the following formula:
\frac{\partial L}{\partial ψ} = \sum_{i=1}^\infty \frac{\partial (\frac{\partial L}{\partial ψ_xi})}{\partial x_i}
where x_i...
thank you very much tia89. I really appreciate your help. I think I will go for dark matter and dark energy since a lot of researches are being done in these fields recently.