"A number of important properties of the scattering amplitude can be established by considering it as a function of the energy $E$ of the particle undergoing scattering, the energy being formally regarded as a complex varriable."
@bolbteppa sure. you'd expect to have poles at the bound state energies, if memory serves.
@0ßelö7 and if you're doing scattering in a periodic potential, then you'll have bands of allowed/ forbidden energies. I think in that case the scattering amplitude has square root branch points at the band edges? I'm not certain that's right, though.
@EmilioPisanty could we have an automated system to warn of posts about career suicide e.g. questions about the interpretation of quantum mechanics :-)
so, if i post an answer to a homework question on the main site expression frustration towards OP's zero attempt and say "i have level 4 cancer; i want to die now", do i get to have a personal email?
I'm not sure I would really read it as actual suicide talk (looks more like taking the mickey than anything else), but yeah, there's no harm in treating it in full seriousness
In section 3.1 of The Wave Equation on a Curved Spacetime, Friedman defines what a characteristic hypersurface for the wave equation $$\Box u+a\cdot\nabla u+bu=f$$
is, and then shows that these are precisely the null hypersurfaces of the Lorentzian manifold. He also talks about tensor wave equati...
Does anyone know the derivation of the Arrhenius equation? I couldn't find it on the internet. Or, are we simply supposed to learn it without deriving it?
when I try to compile it on MSVC I get: error C2065: 'i': undeclared identifier rat.c(6): error C2057: expected constant expression rat.c(6): error C2466: cannot allocate an array of constant size 0 rat.c(6): error C2133: 'input': unknown size
Hmm..well if you add the iterator of Reinman function and couple it with dimensional instability of Wittenian manifolds, it gives you a globally stable field.
@Koolman in standard C or C++ you cannot declare an array with a variable length. You need to allocate the memory for the array using malloc or for C++ new
I believe GCC has extensions that do allow for variable length array declarations
@Qmechanic Jon was saying they have a policy of responding to all posts that look related to suicide, and it makes sense to assume they're real. If they aren't there's no great harm done.
@Koolman I would say that Kernighan and Ritchie is good for newcomers to C that already have at least a little of the programmer mindset. It often overwhelms complete newbies.
In any case you have to read the book carefully as there are many places where each word is chosen for a reason (as is each word left out).
@Abcd I think it depends on what you count as a 'derivation.' One can certainly obtain it by starting from certain assumptions/approximations, e.g. Arrhenius's logic about activation energy. But if you don't include those approximations then you probably won't get such a simple result. (And you can find systems that will violate it; google 'non-arrhenius behavior' for examples.)
It's a bit like Ohm's law in that regard, I suppose.
What exactly does this mean? Could I be banned from asking questions just for clearing out trash / malformed questions that received answers that are just of the form "Your premise is wrong" or Duplicates? I could maybe understand the virtue of leaving the former up so anyone else caught in the s...
Hello! I have a professor that described one stream of light traveling through a birefringent medium as going "slower" than the other, but this is making no sense to me. Is there another word besides slower that would better describe this?
The tricky word in here is really velocity and what that means for a ray of light
citing WP for convenience: "The refractive index n of an optical medium is defined as the ratio of the speed of light in vacuum, c = 299792458 m/s, and the phase velocity v of light in the medium, i.e. n=c/v. The phase velocity is the speed at which the crests or the phase of the wave moves, which may be different from the group velocity, the speed at which the pulse of light or the envelope of the wave moves."
I was not aware that there was a phase and group velocity... this is probably why I was lost. Would one of these velocities stay constant? For example: the phase velocity of light is always the same, but the group velocity can differ when passing through different materials.
the point, I suppose, is that while light doesn't have a medium, it does interact with its environment. hence light propagating in vacuum need not behave the same as light propagating through glass, for instance.
mercifully, in the case of glass it mostly behaves the same, but with a lower velocity than you'd get in vacuum
there are other media which are weirder in that regard.
the fashionable example nowadays are metamaterials, but that would definitely be outside the context of mineralogy
hmmm
ah, actually, your birefringent query originally is an example:
"Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light."
setting aside the polarization part, the propagation direction bit is clear enough: if you send in the light horizontally, it can take longer to pass through the medium than if you did so vertically.
There's a macroscopic vs. microscopic question here, though. Macroscopically it's enough to say that, for whatever reason, a birefringent material exhibits a difference index of refraction for light entering vertically vs. horizontally.
@Semiclassical With two different rays entering the object, the propagation direction difference makes sense. From what I understood from the lecture, one ray of light was entering at the same position, separating into two different rays, and then recombining to form an interfering wave that was different from the original. Would this be where the microscopic explanation would be of use?
but this goes to a word that I put aside earlier: polarization
one usually talks about either linear or circular polarization of light; the latter is more annoying, so I'll only address the former.
the basic point is that what constitutes light, at the macroscopic scale which matters for crystals, are electric and magnetic fields which vary in space and time
@Avantgarde why cant rest mass be a variable? for refrence i'm considering the equation $E^2=m^2c^4+((1/sqrt(1-v^2/c^2)mv)^2c^2$ which seams to accept m as a variable
(continuing from above): but nothing is stopping us from having the electric field pointing in a different direction; we could swap the blue and red vectors and that'd still be a valid light wave, just with a different polarization
(continuing) Additionally, we could take two waves with different polarizations and take their superposition. Then we'd get a light wave which is a mixture of the two polarizations
@shaihorowitz I think you mean the 'relativistic mass', which is different from the rest mass. Some people don't like talking in terms of relativistic mass because it can provide an incorrect picture of what happens to a particle's energy content at different velocities. In any case, you're right, this is classical mechanics (with special relativity) and there are no operators here, so commutability follows.
now suppose we shine unpolarized light on an optical medium. if the material isn't birefringent, then nothing terribly weird happens: each polarization of light has the same velocity in the medium, and so they all refract in the same way.
but if it's birefringent, then that's not the case and each polarization can have a different index of refraction.
in the end, i'm trying to consider a mass-less particle gaining mass. so i have to worry about quantum commutabillity only in the sense that i need to make sure i'm not leaving out a part of the system. in that sense i care about the variables (m,v) and (S,T)
and therefore the different polarizations will refract with slightly different angles at the interface of the medium
now, why different polarizations of light behave differently in that that question is another question entirely. but if it can happen, then you get various experimental consequences
@Semiclassical You guessed correctly what my next question would be... but considering that this topic is now delving into the realm of "oh god" flashbacks, I won't harass you any further. You already helped me understand polarization of light much better. Are there any good books I could pick up to understand the details better?
i'm saying you can define temp that way. and entropy as a measure of macro states. in this sense they become quantum operators. i'm asking if these specifically commute
In philosophy, a razor is a principle or rule of thumb that allows one to eliminate ("shave off") unlikely explanations for a phenomenon.
Razors include:
Occam's razor: When faced with competing hypotheses, select the one that makes the fewest assumptions and is thus most open to being tested. Do not multiply entities without necessity.
Grice's razor: As a principle of parsimony, conversational implications are to be preferred over semantic context for linguistic explanations.
Hanlon's razor: Never attribute to malice that which can be adequately explained by stupidity.
Hume's razor: "If the cause...
I initially read
> Do not multiple entities without necessity.
but it's not like correcting it makes it that much better
@Semiclassical I told the organizer for the seminar that I'd have a somewhat outline by Monday. These talks aren't out of the blue and it's well within my field.
Let $M$ be a smooth manifold and denote $C^\infty_0(M)$ the space of smooth functions with compact support. In Mathematics a distribution is defined to be a continuous linear functional $\phi : C^\infty_0(M)\to \mathbb{R}$. The space of distributions is usually denoted $\mathfrak{D}'(M)$.
So a d...
I don't think there exists something like infinite dimensions for dummies, because infinite sets and functional spaces requires quite high level maths to understand
Unrelated, but I also suspect had we humans need to deal with infinite sets on a daily basis, then finite number mathematics will still be easier to us. If we had already being able to count to infinity, then finite is a very very small number and possibly all finite maths will have been done in an instant