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1. How do I see if the equations of motion are satisfied?

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...
2. A What is orientation of a needle shaped spacecraft?

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...
3. Cylinder parallel to a constant external B field

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...
4. Canonical Transformation (two degrees of freedom)

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...
5. Finding canonical transformation

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...
6. Collision of two photons using four-momentum

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...
7. Separation of variables and potential

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...
8. Quantum mechanics operators

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...
9. Finding potential using Greens function

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...
10. Can we make use of Greens function if there are no charges?

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...
11. Partition function

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...