Homework Statement
Show that the radiation field is transverse, ##\vec{\nabla}\cdot\vec{A}=0## and obeys the wave equation ##\nabla^2\vec{A}-\frac{1}{c^2}\partial_t^2\vec{A}=0##. You should start from the expansion of the quantum Electromagnetic field.
Homework Equations
##H=\frac{1}{2}\int...
Homework Statement
Exact spin symmetry in the Dirac equation occurs when there is both a scalar and a vector potential, and they are equal to each other. What physical effect is absent in this case, that does exist in the Dirac solution for the hydrogen atom (vector potential = Coulomb and...
Sorry, I forgot to mention that the electrons interact through a coulombic potential ##V=-e^2/r##. Two electrons can't be in a bound state attracting each other through this potential, as far as I understand.
Homework Statement
If a system comprised only of two electrons was physically possible (such as positronium but with two electrons), what would its energy levels be and how would they relate to the energy levels of Helium?
Homework Equations
##E_{Helium} = E_{n1}+E_{n2}=-\frac{\mu Z^2...
Actually he said he can't even tell me where it is documented because he's never worked on what he wants me to do, he just wants me to figure it all out on my own. So do you think I should choose a different project with a different supervisor?
I forgot to mention that I was working with my supervisor and he can give me access, but he made it clear that he won't help me understand the code. He was the one who chose calorimeters and LHCb. I just need to know if once I have access there is any way I can make sense of it if I have no...
I want to do a project using machine learning on the calorimeter event data of the LHCb. How can I access this data? Is it very difficult to navigate your way through the source code on your own?
Homework Statement
Consider the Klein-Gordon equation ##(\partial_\mu \partial^{\mu}+m^2)\varphi(x)=0##. Using Noether's theorem, find a continuity equation of the form ##\partial_\mu j^{\mu}=0##.
Homework Equations
##(\partial_\mu \partial^{\mu}+m^2)\varphi(x)=0##
The Attempt at a Solution...
Homework Statement 1. Homework Statement [/B]
Prove the potential energy of interaction between an electric charge ##q## moving with velocity ##\vec{v}## and an electromagnetic field with potentials ##V## and ##\vec{A}## is given by ##U = qV-q \vec{v} \cdot \vec{A}##
Homework Equations...
Thank you very much, I had the feeling something was wrong when the math just didn't agree with the statement.
Do you know of any property that is similar to the one I was trying to prove? I mean, if the problem is mis-stated, any ideas as to what the correct statement is?
Homework Statement
Prove that a current density J(r, t) such that ∇ × J = 0 implies the magnetic field B = 0.
Homework Equations
Maxwell's equations, vector calculus
The Attempt at a Solution
I've played around with Maxwell's equations and with the properties of vector calculus but I...
Homework Statement
In a region of empty space, the magnetic field is described by ##\vec{B} = B_0e^{ax}\sin{(ky-\omega t)} \hat{z}##. Find the speed of propagation ##\vec{v}## of this field.
Homework Equations
##\Delta \vec{B} = \frac{1}{v^2}\frac{d^2\vec{B}}{dt^2}## , ##k=\frac{\omega }{...
Not really, it just says that the probability is that of Brownian movement and we are asked to find that relationship as preparation to derive and solve the diffusion equation.
Homework Statement
Consider the diffusion of a drop of ink in a water vase. The density of the ink is ## \rho (\vec{r}, t) ##, and the probability ##P(\vec{r}, t)## obeys the diffusion equation. What is the relationship between ##\rho (\vec{r}, t)## and ##P(\vec{r}, t)##?
Homework Equations...
Homework Statement
Two coplanar dipoles are oriented as shown below.
If θ is fixed, what is the equilibrium angle θ' ?
Homework Equations
The torque exerted by dipole P on dipole P' is given by $$\vec{N'}=\vec{P'}\times\vec{E}$$ where vector E is the electric field.
The Attempt at a...
Homework Statement
Try to estimate the latent heat of vaporization of water and nitrogen using the Van der Waals model. What happens?
Homework Equations
$$ΔQ=TΔS=L$$
$$S=nR[\ln(\frac{(V−nb)T^{3/2}}{nΦ})+\frac{5}{2}]$$
The Attempt at a Solution
I predict the latent heat of vaporization of...
Homework Statement
Try to estimate the latent heat of vaporization of water and nitrogen using the Van der Waals model. What happens?
Homework Equations
$$\Delta Q = T\Delta S=L$$
$$S=nR\left[ \ln\left(\frac{(V-nb)T^{3/2}}{n\Phi}\right)+\frac{5}{2} \right]$$
The Attempt at a Solution
I...
Homework Statement
Obtain the chemical potential of water as a function of temperature and volume using the Van der Waals model.
Homework Equations
μ=∂U∂N
The Attempt at a Solution
I don't really understand how to do this at all. Any help would be greatly appreciated.