From a purely classical EM theory viewpoint, you only need a temporally equally short 'pulse' of current at some point and the only thing that Maxwell's equations do is prescribe how the resulting em-field propagates. But they do not forbid you to create any kind of however short temporal...
I am not completely sure if i understand the question correctly.
One likes to change the basis from the position to the momentum basis, because the momentum basis is an eigen-basis ie the plane waves are eigenstates of propagation and it is thus easy to calculate their time-evolution.
So...
An addition about the photons: I think you can also generate states where each photon is in a superposition of frequencies (=colors) so even the single photons can be "white".
I don't know however if this is the case in your usual white light.
The case of several photons with one wavelength each...
The discrete eigenvalue spectrum basically counts how many (eigen-)solutions there are (finite, discretely infinite, continously infinite).
It does not say anything about wether those solutions themselves are continuous or discrete!
In qm i actually can only think of examples where the...
Only the speed of light in vacuum is constant.
If a wave propagates in a medium it drives the electrons to oscillate around the core. Due to this movement of charges new waves are excited at each atom site.
All the waves taken by themselves oscillate with the vacuum speed of light, however when...
To question 1: the solutons of the schrödinger equation corresponding to the energy levels of an atom are supposed to be solutions that are constant (except a phase factor) over time (== eigenfunctions of the hamiltonian). That's intuitive i guess, because they are supposed to be "stable...
I originally studied computer engineering and am now trying to do a PhD in (mostly computational) physics. This might be a possibility for you if you find an advisor who is willing to hire you.
I am doing nanophotonics, but i guess for a computer scientist with a good numerics background any...
When i once looked up nonlinear wave equations and solitons for recreational purposes i got the feeling that what you are looking for should be the Korteweg- de Vries Equation
http://en.wikipedia.org/wiki/Korteweg%E2%80%93de_Vries_equation
I don't know much about the topic, but the...
To the first question:
A "physical" wave can be measured in terms of pressure (in the case of the example with springs or a sound wave in gas), or electrical fields / intensities (in the case of the EM field).
A QM wavefunction is actually a probability amplitude for the position (or other...
The example in the end of your post, ie oscillating particles that are coupled to each other, are precisely what sound waves are. You can actually model them with coupled harmonic oscillators (or better with mass points with springs in between).
If you have a charged particle and wiggle it, you...
Thanks a lot! I see now, that one can calculate the vector potential from its wave-equation and then use the gauge condition to get the scalar potential from the vector potential.
I also tried this out numerically and actually got what looks like a dipole when calculating the electric fields...
Thanks so far! If i interpret your answers correctly, my initial guess was correct and in the potential formulation it is important to model sources correctly, explicitly including charge conservation when introducing a current as a source. This will generate not merely a vector potential, but...
If in a volume of plasma (or in a metal) the electrons get separated from the positive charges (for example by applying an external electric field), an electric field will build up due to the charge separation. This in turn, will pull the charges back together. They will overshoot and the system...
I think the point is, that a vector space is defined as a set and some operations defined on the set, which in the end obey the same rules as the "traditional" vectors. Actually i had to prove/disprove the vector space axioms for lots of sets and associated operators in school and again at the...