Dear all,
I don't know how or why but I've managed to get shortlisted for two DPhil interviews in Oxford, both of which are related to two separate projects I wish to do (one is in Quantum Electronics, the other in Computational Quantum Mechanics).
I am to firstly talk for 10 minutes about my...
Hey all,
I'm a final year MEng student in engineering physics (a very broad degree) at a recognized Scandinavian technical university. I'm deciding what to do with my life, and my personal dream is to get into business in the long term, preferably in something high-tech that's growing...
Hey guys
So I'm sure there are plenty of threads about what people think are the most exciting subfields, but what about the most boring? Which subfield of physics did you enjoy the least learning?
I'll begin. In my opinion it has to clearly be scattering theory & everything related (e.g...
Hey all,
Is it correct to say that magnetic moment of particles with spin is because of the spin itself, and has nothing to do with any moving charge? The exception here would be the photon of course, but I'm not sure whether "photon spin" is the same kind of angular momentum as the spin of...
Hey guys,
I have an interview with BCG, https://en.wikipedia.org/wiki/Boston_Consulting_Group, next friday and I'm just wondering if any of you have experience with this company and have any tips? Till now I have been doing cases, reading a caseinterview book and practicing mental math, but I...
Hey all, I'm having some issues with electromagnetism here.
Let's say we have a particle with magnetic moment ##\vec{\mu} = \mu_0 \hat{x}## and magnetic field ##\vec{B(x)} = B_0 \frac{x}{a} \hat{x}## where ##\mu_0,B_0,a## are constants.
If we assume that the magnetic field ##B_0## is far, far...
Hi, suppose two players are a playing a game with a non-square payoff matrix, like for example this one:
.....a.......b...
A: (1,3) (1,0
B: (0,0) (2,1)
C: (3,1) (0,3)
How would one go about finding an optimal mixed strategy for something like this? I mean, if this was a 3x3 matrix then one...
Hey! I'm reading Special Relativity right now and I am stuck trying to understand tensors. Can you kind people please explain to me the difference between the following 3 tensors?
$$A^{\alpha \beta}$$ $$A_{\alpha \beta}$$ $$A^{\alpha}_{\beta}$$
Mod note: Moved from technical math section, so no template was used.
Hey! So the complex fourier transform of the square wave
$$
f(x) = \begin{cases}
2 & x \in [0,2] \\
-1 & x \in [2,3] \\
\end{cases}, \space \space f(x+3) = f(x)$$
is ##C_k = \frac{3j}{2 \pi k}( e^{-j \frac{4 \pi k}{3}}...
Homework Statement
It's problem 4:[/B]
https://scontent-sea1-1.xx.fbcdn.net/hphotos-xpa1/v/t1.0-9/12004675_10206509414950788_2644752353357758096_n.jpg?oh=e6292fae7cdc34b881c7ac31a506e315&oe=56680268
Homework Equations
The Wiener Khinchin theorem gives that the normalized spectral power...
For a good conductor, an incoming plane electromagnetic wave will be attenuated exponentially as it penetrates a distance ##z## into the conductor, ##|\vec{E}(z)| = |\vec{E_0}|e^{-z/ \delta}##. ##\delta## is called the "skin depth". The current generated by this incoming electromagnetic wave is...
Homework Statement
[/B]
Homework Equations
https://en.wikipedia.org/wiki/Clebsch–Gordan_coefficients
I don't know how to calculate tensors though..
The Attempt at a Solution
OK so how do I even proceed? All I know about Clebsch-Gordon coefficients is that you can use them to calculate...
Hey!
How are the two m=0 spin states (<up,down> + <down,up>) and (<up,down> - <down,up>) physically different? I realize that according to the math, the first one has a total spin of ##2 \hbar## while the second has a total spin of ##0##. But wouldn't you, intuitively, expect both states to...
Hi!
If I have understood things correctly, in a multi-electron atom you have that the spin operator ##S## commutes with the orbital angular momentum operator ##L##. However, as these operators act on wavefunctions living in different Hilbert spaces, how is it possible to even calculate the...
Homework Statement
See uploaded file.
Homework Equations
I guess one needs to keep in mind this:
https://en.wikipedia.org/wiki/Complete_set_of_commuting_observables
The Attempt at a Solution
Basically, my question is about the notation:
1) What does the subscript "ee" stand for in H_ee? And...
Hey.
Assume you have a signal ##f## with period ##T_f## and a signal ##g## with period ##T_g##. Then the signal ##h= f+g## is periodic iff ##T_f/T_g \in \mathbb{Q}##.
So if ##T_f/T_g## is an irrational number, the signal ##h## will not be periodic. Why is this actually the case?
Hi all.
I'm struggling with taking dot products between vectors in spherical coordinates. I just cannot figure out how to take the dot product between two arbitrary spherical-coordinate vectors ##\bf{v_1}## centered in ##(r_1,\theta_1,\phi_1)## and ##\bf{v_2}## centered in...
Hi! How exactly is the relationship between number of atoms in the basis of a bravais lattice, and the number of possible phonon modes?
So, for example, if you have 2 atoms in a basis you get 3 acoustical and 3 optical modes in 3 Dimensions. But why exactly is this? Do you need to set up the...
Hi! When we model bloch-waves in a solid we assume that there exist some kind of periodic boundary conditions such that the wave function is periodic. In 1D, ##\psi(x)## repeats itself for every ##L##, ##\psi(x) = \psi(x+L)##, such as here:
OK, fine, we get pretty wave solutions if we assume...
Hi! I would like to ask some general question about IR spectroscopy.
During absorption of IR photons two quantities have to be conserved, energy ##\hbar \omega_{photon} = \hbar \omega_{phonon}## and momentum ##\hbar k_{photon} = \hbar k_{phonon}##.
Wouldn't these two quantities be conserved at...
Hi! According to this http://en.wikipedia.org/wiki/Electrical_mobility, the definition of electrical mobility ##\mu## is:
##\vec{v} = \mu \vec{E}##. But since electrical mobility is always positive, this means that the velocity is always parallel to the E-field regardless of charge. How can...
Hi. Here's the dispersion relation for a diatomic linear chain, where the distance is a/2 between each atom.
My issue here is that if you set m_1=m_2=m, i.e. set both atoms equal to each other, it doesn't automatically reduce to the old acoustic dispersion relation as the ± term doesn't...
Hi! I feel like I've understood none of this stuff!
A 1D chain of springs and masses modeling a chain of atoms has a dispersion relation ala ## \omega## ~ ##|sin(k a /2) |##, where ##k## is the wave vector and ##a## the distance between atoms. As far as I have understood, the debye model (in...
Hi. This might be a stupid question (I'm studying engineering :p), but how do you prove that all numeral systems (binary, ternary etc.) can represent every countable number?
I guess you will need to prove that any number ##N## can be written as ##N= S^0 n_0 + S^1 n_1 + S^2 n_2 + ...## where...
Hi. Say we have found a hamiltonian ##H## for some system.
So I know that if ##\frac{\partial H }{\partial t} \neq 0## then obviously the energy of the system is not conserved.
But if ##\frac{\partial H }{\partial t} = 0##, is the energy always conserved? Or do we need to find that ##\frac{d H...
Hi.
According to classical electromagnetism (and common sense) the intensity of a beam of light entering a dielectric medium should remain constant. Hence the length of the poynting vector must remain constant.
But how do you derive mathematically the last point? Because if you just replace...
Hi!
Assume paraxial rays. If I have a lens with a focal length ##f## and I place an object at the focal length to the left of the lens, the image will be at infinity. Correct? But will it be imaged in infinity to the left or right of the lens?
If I am looking into the lens from the right I...
Hi!
While testing my knowledge of analytical mechanics I stumbled across a fallacy that I am unable to resolve. Could you assist me?
When you finish integrating a Lagrangian over the time domain ##[t_1,t_2]##, shouldn't its position ##q(t)## and position dot ##\dot{q(t)}## variables take the...
Here's a problem I am doing right now.
What are the cofactors " ## \Delta_{i \alpha} ##"? I know they are represent the minor of some determinant, but I am confused and can't see which determinant it is.
Also, could somebody please help me and explain why ## ( V_{ij} - \omega^2 T_{ij} )...
Hi. A spherical wave ##e^{i(kr-\omega t)}## diverging from a single point ##(x=0,y=0,z=-z_0)## can be approximated as a parabolic wave in the paraxial case around the z-axis. I.e., ##k r = k \sqrt{x^2+y^2+z^2} \simeq k (z +\frac{x^2+y^2}{2z})##.
OK, then let's say a lens is placed such that its...