I'm just going to ramble off some observations and thoughts of mine relevant to the question.
First of all, I want to point out that most classes are essentially theoretical (i.e., most classes aren't labs.) These classes are taught by both experimentalists and theorists. So the apparent...
I am considering a second order ODE of the form y''(x) + f(x) y(x) = 0, with boundary conditions that y(x) = 0 at plus/minus infinity. Note that f(x) is complex for my case.
It seems that the standard techniques for numerically solving this problem are (a.) the finite difference method and...
Could you help point me to one of these solutions then? I don't recall ever seeing the time-dependent Schrodinger equation solved for transitions or ionization and I'm not sure where to look...
Nevermind. I just forgot for the red-box FBD you still have to include the weight of the mass, so actually it just says the tension in the top rope is equal to twice mg again. Doh. Too long since I did basic physics.
I have a basic pulley problem which has been troubling me.
Consider the system as shown in the attached picture. We have a massless pulley attached to the ceiling and a mass suspended from one side of the pulley.
If we take the free-body-diagram by 'cutting' where the red box is, we find...
I'm thinking that maybe my suggestion above doesn't work, so let me rephrase/restate my question.
Say we want to define a vector field in R^3. Then we need a way to consistently define a directional basis at each point, and a position for each point. The common choices are well known --...
Say we have a vector field defined in R^3. That is, at every point p in R^3, we have the corresponding set (p, v(p)). In representing this field, as far as I can tell, we have a certain list of very general requirements. That seems to be
a.) an origin,
b.) three everywhere non-coplanar curves...
Wow Fredrik, that's an outstanding response... thumbs up...
Regarding question 3 --
This resource "http://homepages.cae.wisc.edu/~callen/FluxCoordinates.pdf" [Broken] is frequently used in my department for introducing the notions of "covariant components" and "contravariant components"...
Having been through a through a number of textbooks, I can say without reservation Jackson is one of the best books I have studied. Some books are simply incomprehensible (leaving out details in the derivations, omitting crucial facts, speaking in confusing language, speaking unclearly). Some...
OK, thank you for that review. For my own edification I will make a few comments or remarks now. I thought that a chart just had to be smooth -- I didn't realize that we actually only require the weaker condition that the chart only needs to be smoothly compatible.
Also, I suspected that the...
Ah yea, sorry, I meant to say *smooth*, not continuous.
Regarding your answer -- I don't understand, or maybe I am not understanding what it means for this map to "generate" the differentiable structure. As I understand it, this map x^3 will act just like a chart; so therefore it must be a...
I'm not sure what a Peano curve is, but I know a simple case where you can have this to be true. If you take a toroidal curve with an irrational rotational transform (the ratio of poloidal period covered in one full toroidal period), then as the number of transits goes to infinity, this curve...
Consider the manifold of the real-line R with a differentiable structure generated by the map x^3 : M \rightarrow \mathbb{R} . This example is given in a textbook I'm looking at, but I don't really understand how this can work. The inverse map is clearly not smooth at x=0.
Do they mean that...
Ah, ok, I see. That's more or less what I was thinking I just wasn't sure how to express the details correctly. I also get how the U_v's form an open cover in the induced topology, I just thought that maybe they were saying they were also open in the general topology. Thanks for the the help.
First of all I just want to rant why is the Latex preview feature such a complete failure in Firefox? Actually it is really bad and buggy in IE too....
So I am reading into Foundations of geometry by Abraham and Marsden and there is a basic topology proof that's giving me some trouble. They...
Are you familiar with a solenoid? This is simply a device which is used to project a magnetic field in a certain direction, like you are saying. Of course you can put a bunch of solenoids together to focus fields, or you can send the magnetic field further out by increasing the current running...
Say you have two functions, F(x,y), and G(x,y), and you want to expand them in finite fourier series. Let their coefficients be designated as F_ij and G_ij. When you multiply the two functions, you get X=FG, and this should also have its own fourier series, call its components X_mn. What is the...
Well, you get the accelerations from the Lagrangian, T - V, which only includes terms proportional to q and q-dot. The uniqueness of the solution will come from the theory of ODE's, like George Jones says.
Infinite instantaneous values of acceleration are not really relevant here, since they...
In this problem, the v x B force is generating an electric field which gives you an electromotive force. But that doesn't mean the v x B force acts nonconservatively. See below.
I'm not at all convinced by your arguments in this claim. The work being done to expand the wire area is the force...
OK, gotcha. To summarize, I think you are saying that once the spin magnetic moment or orbital magnetic moment of the electron reaches the ionization energy, that is when (in principle) the electron would escape. Could you possibly comment on how the spin energy or orbital energy would cause an...
I'm interested in the question of what strength magnetic field you need to fully or partially ionize a neutral atom. I'm fairly sure this is possible but I'm not very familiar with quantum physics, atomic physics, solid state physics, and so on. I'm familiar with the "classical analog"...
It's a pretty difficult problem. I suffer from it a lot... it's a personality thing, but it's completely normal for a lot of people, so you shouldn't feel weird or embarrassed or anything. I would recommend reading "Zen and the art of motorcycle maintenance", as he talks a little bit about these...
Another easier, possibly more correct way to say this is the following. The equation you give above (the same one in my post above) uses v to refer to the loop velocity. That is not the Lorenz force there in that equation! The Lorenz force refers to the velocity of the charges. Now, the loop...
Consider the equation you show from your book,
(*) int([v x B] .dl) = - int(B. [v x dl]) = - d(phi)/dt .
The confusing point in this problem/equation is that the v variable doesn't discriminate between the v charge in (1.) the charge carriers of the original, unchanging circuit, and (2.) the...
Not to derail the initial discussion, but I just want to let it be restated that the user Integral deleted another user's post in this discussion. That user wasn't going into original research and I've never seen anything like that on the physics forums before. The deletion of a well intentioned...
Yea, if you work out the "d" operator applied to a coordinate function x^i, you see that the dx^i are identical to the covector basis a^i, where a^i are just the functions such that a^i(e_j) = delta_ij.
Anything that is time dependent is frequency dependent, and vice versa. If you just Laplace transform a time dependent variable you will get fields that are frequency dependent. It just depends on how you want to look at it. The poynting vector is most definitely frequency dependent. Not exactly...
Depends on your budget. I just did a little random digging and found a few torches here: http://www.bernzomatic.com/quickfire-hand-torch/quickfire-faqs.aspx. These cost about $70 per pop, but it says they go to 3600 deg F. You could get 2 of these guys, and an outdoor wood stove, drill a few...