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...
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...
@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...
the problem is on page 26 of "relativistic quantum mechanics and field theory" by Franz Gross.
consider the lagrangian density:
L=(1/2)[(∂ψ/∂t)^2 -(∂ψ/∂z)^2 -m^2ψ^2]
a) find the momentum conjugate.
b) find the equation of motion for the fields and the solution. use periodic boundary...