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...
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...
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...
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 }{...
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.
Question:
If L is a Lagrangian for a system of n degrees of freedom satisfying Lagrange's equations show by direct substitution that
http://qlx.is.quoracdn.net/main-74d090d14ee4fea0.png [Broken]
also satisfies Lagrange's equations where F is any arbitrary but differentiable function of its...
Homework Statement
A two component gaseous system has a fundamental equation of the form
$$S=AU^{1/3} V^{1/3} N^{1/3} + \frac{BN_1N_2}{N}$$ where $$N=N_1+N_2$$
and A and B are positive constants. A closed cylinder of total volume 2V_0 is separated into two equal subvolumes by a rigid diathermal...