At undergraduate levels, it is usually treated as such. However, the PEP (and for that matter, spin itself) is a direct consequence of relativistic QM, and falls naturally out of the theory.
It has to do with the fact that for fermions, the wavefunction for two particles must be antisymmetric. If they were both in the same state, then the wavefunction would cancel out to zero, which does not make any sense physically.
You type it up in a regular text file, then save it with a .tex extension. Then, you need to compile it by typing "latex file" (no quotes, in Windows, at a DOS prompt, in the directory where the file is saved), where file.tex is the thing you just saved. This will generate a DVI file. With...
The product rule applies fine for a constant term, since a constant is a perfectly good function. It does not apply the way he said though; his exponential relation is wrong.
e^ne^x=e^{n+x}
Hard to say. Certain areas (such as optics, nanotechnology, etc) have a wider range of applications, and can offer jobs in both academia and the industrial sector.
Generally, if you're going into physics to make money, then you're going into it for the wrong reasons.
Nanoparticles are just small clusters of some material, made up of a "small" number of atoms, and exhibiting sizes on the order of a few nanometers. The difference in properties between the nanoparticles and bulk systems arise from many different phenomena, such as quantum confinement.
An...
- I suppose classical concepts can be easier to deal with in some cases.
- Quantum is dominant at small size scales, classical at large ones. It depends on the situation and your assumptions.
- Both. Again, it depends what you're talking about. In many cases, classical physics gives a...
When an external field is applied to a diamagnetic substance, screening currents occur to oppose the external field; that is why the induced "dipoles" align opposite to the applied field. Paramagnetic behavior is due to permanent dipoles aligning to the field, reducing the total energy.
\ln(x+5)=\ln(x-1)-\ln(x+1)=\ln\left(\frac{x-1}{x+1}\right)
So,
x+5=\frac{x-1}{x+1}
Solve this for x, and you will see that both possible values generate a negative argument in the second logarithm, so there is no valid solution.
Also, I am guessing you are considering the case where 0<E<V. In that case, you might want to check your energy constants. They should probably be
k=\frac{\sqrt{2mE}}{\hbar}
\kappa=\frac{\sqrt{2m(U_0-E)}}{\hbar}
Your solution inside the well would then be
\psi=Ae^{\kappa...
Things are looking pretty good so far. For your function before the barrier, it is usual to include normalization on everything, including the first exponential term (unless you have been told specifically not to).
\psi=Ie^{ikx}+Re^{-ikx}
Other than that, it is a matter of dregding through...
Once in the superconducting state, all magnetic flux is expelled from the interior of the material. This is a result of screening currents on the surface which counteract the external field. This is similar to what happens in typical diamagnetic materials.
A BEC is made up of bosons (as the name suggests) which have completely different properties than the fermions (electrons) in a SC. There are two completely different phenomena at work.
BECs are not superconducting (as far as I know). The repulsion of magnetic fields from a SC is an entirely different effect than using magnets to trap atoms in the condensate.
Once a superconductor is cooled below its critical temperature, its reistance drops to 0. This coincides with the production of Cooper pairs, as you mentioned. As the name suggest, a Cooper pair is two electrons, which "join" in such a way that the total spin cancels out. In this way, a Cooper...
You say tomato, I say tomato.... I usually just use quanta for everything, singular or otherwise. I guess I should pay more attention :wink:
BTW krab, I noticed in your profile that you work at TRIUMF. Very cool. My thesis research is currently based on μSR experiments conducted there.
You might me thinking of quanta. A quanta is a small piece of something. It is commonly used to describe something that is not continuous but quantized (hence the name). For example, the quanta of the electromagnetic field is a photon. Similarily, phonons are the quanta of vibrations inside...
You're right, it is a confusing topic. Some books use B as the magnetic field, others H. Basically, think of B as the magnetic field, like you are used to. H is introduced mostly as a convenient way to rearrange Maxwell's eqs. Specifically, it allows you to write the eqs in terms of something...