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  1. M

    The Should-I-Become-A-Theoretical-Physicist-or-Experimental-Physicist? Thread

    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...
  2. M

    Shooting method vs. finite differences for BVP

    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...
  3. M

    Ionizing solutions to the hydrogen atom

    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...
  4. M

    Ionizing solutions to the hydrogen atom

    I mean a solution where the electron transitions from being bound to breaking away... like in a collision.
  5. M

    Ionizing solutions to the hydrogen atom

    Are there any ionizing solutions for the hydrogen atom problem, where the electron breaks away from the proton?
  6. M

    Contradictory FBD's for simple pulley problem

    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.
  7. M

    Contradictory FBD's for simple pulley problem

    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...
  8. M

    Generic coordinate systems

    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 --...
  9. M

    Generic coordinate systems

    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...
  10. M

    Some Questions About Tensors

    Wow Fredrik, that's an outstanding response... thumbs up... Regarding question 3 -- This resource "" [Broken] is frequently used in my department for introducing the notions of "covariant components" and "contravariant components"...
  11. M

    Physics Grad Programs that don't require Jackson's Electrodynamics

    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...
  12. M

    Example of a differentiable structure on R

    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...
  13. M

    Example of a differentiable structure on R

    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...
  14. M

    Infinite curve with two endpoints?

    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...
  15. M

    Example of a differentiable structure on R

    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...
  16. M

    Compact sets in Hausdorff space are closed

    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.
  17. M

    Compact sets in Hausdorff space are closed

    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...
  18. M

    Can magnetic fields be focused to distant points?

    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...
  19. M

    Multiplication of fourier series

    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...
  20. M

    Landau Lifshitz's statement on Coordinates, velocity & acceleration

    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...
  21. M

    Origin of non-conservative Faraday

    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...
  22. M

    Ionization by magnetization

    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...
  23. M

    Ionization by magnetization

    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"...
  24. M

    Why can't I study ?

    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...
  25. M

    Origin of non-conservative Faraday

    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...
  26. M

    Origin of non-conservative Faraday

    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...
  27. M

    Need help explaining light speed limit to younger brother

    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...
  28. M

    Differential Geom.: Dual Space Bases for Beginners

    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.
  29. M

    Is the Poynting Vector Frequency Dependent?

    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...
  30. M

    How to reach 2,000 Fº at home?

    Depends on your budget. I just did a little random digging and found a few torches here: 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...
  31. M

    Understanding in abstract algebra

    Chaz -- you're right, sorry, chain rule is obviously a result not a definition, I was just speaking crudely.
  32. M

    Understanding in abstract algebra

    In algebra, do you just base your understanding off the pure definitions and groups? I am learning some multilinear algebra, seeing a lot of talk about rings, algebras, modules, etc. and I can't help but thinking it's all just frivolous, pointless definitions. That's partly because I just can...
  33. M

    Investigating Energy Conservation with Sinusoidal Waves

    Notice that for phi=pi, you just have y1=Asin(kx-wt) and y2=-Asin(kx-wt). So y1+y2=0 and you actually don't have a wave any longer. The punchline is that you cannot choose whether or not to add up the waves. If two independent waves are both solutions for the same system, then the general...
  34. M

    Problem with the physics behind charged, isolated conductors

    I think this may occur because: If you consider a local positive charge in the center of the volume, it has free electrons around it in every direction that will try to move to nullify the charge. Whereas if you have a local positive charge on the boundary of the volume, there are less free...
  35. M

    No difference between covectors and functions?

    Ahh ok, I think I am understanding, especially the post from dx gets to the heart of my confusion. I forgot that regular functions don't have to be linear, whereas the covectors (or generally k-tensors) are supposed to be multilinear by definition. Thanks a lot.
  36. M

    No difference between covectors and functions?

    I'm reading into an introductory book on manifolds (Tu) and they start out by showing vectors are isomorphic to derivations at a point. They go on to introduce covectors, k-tensors, and then I've just gotten to the point where they introduce the "d" operator which constructs a 1-form from a...
  37. M

    Are functionals united with the vector space which they operate on?

    Lol, this is really funny actually. No offense, but you're not making any sense. :) . These math concepts have very precise meanings... if you want a philosophical discussion, you should ask in the philosophy forum. :)
  38. M

    The relation between angular and linear momentum

    Cleonis, I replied in the other thread because the OP in this post seems a little bit different from what we were talking about there. You may be correct that our disagreement is just about definitions. Anyways -- I agree with you about the interpretation of the angular momentum laws as...
  39. M

    If I roll a hoop forward, what keeps it up?

    No, angular momentum and linear momentum are independent. There are simple mathematical arguments to show this. Anyways, without needing to get into that, even the simplest rotational problems involve the Newton's law of the form I \alpha = M , which is obviously an equation of angular...
  40. M

    If I roll a hoop forward, what keeps it up?

    Conservation of angular momentum is derived by taking the moment of the force equations about some coordinate axis. However, conservation of angular momentum and conservation of linear momentum are distinct.
  41. M

    If I roll a hoop forward, what keeps it up?

    If we imagine a cart on wheels (like a well oiled grocery cart) and we give it a good shove, it will keep moving along in the direction we shoved it. That's the conservation of linear momentum. It follows directly from Newton's laws, meaning that it's a primitive concept. You can't do much more...
  42. M

    Would it Feel as if Time Stopped If I Became Light?

    My area of study lately has been plasma physics, and I find it very interesting to ask myself "What would it be like to be one of the electrons (or ions) zooming around in the field?" For a photon, at the speed of c, I don't know a lot about special or general relativity, but you can at...
  43. M

    Question about falling bodies

    When a ball sits on the surface, it might linger there for a moment because it takes time to accelerate after it's released. There might be some force of adhesion between the ball and the surface. Adhesion depends on the material structure and composition of the ball, surface, and the...
  44. M

    Air resistance on rotating cylinder

    Edit: OK, I looked it over and I'm pretty sure this is all correct now (but I won't make any bets!)
  45. M

    Air resistance on rotating cylinder

    Sorry i had an error somewhere else that might have been throwing you off. I just fixed it and now it should be correct. Actually, the integral is correct because you are evaluating at constant R so you don't need to carry out a radial integration.
  46. M

    Air resistance on rotating cylinder

    You are correct that the drag equation is really derived for the different case of flow going past a body, not for a rotating body. In your next post, you were on the right track I think when you mention the wall shear force of \tau_w = \mu \frac{d u}{dy}. In polar coordinates, the...
  47. M

    Alpha Particles vs. Helium

    Helium atoms are composed of a nucleus with 2 protons, 2 neutrons, as well as an electron shell with 2 electrons. The alpha particle consists of the nucleus alone. The fact they are written the same way is just an example of crappy notation in science. The helium atoms are stable and inert. In...
  48. M

    When to use open/closed set,etc

    This is a question I kind of have myself. I'd like to see some more detailed responses from others... Sorry I'm a math newb. In geometry of curves, they often talk about curves being defined on an open set. In other words, if we think of a plane curve, we would have that \alpha : I...
  49. M

    2 questions about sound - logic reasoning needed

    No, the energy is dependent on the strength of the impulsive load. When the wheel moves faster, this strength increases. Also, the card is not deflected the same amount every time anyways. When the wheel travels faster, it hits the card at faster intervals, and in general, at different states of...
  50. M

    2 questions about sound - logic reasoning needed

    I believe the sound could definitely get louder. Just because the answer wasn't in the assessment doesn't mean you are wrong. It could just be the writers didn't think it was important, or something else. Think of a situation with a hammer and a piece of sheet metal. When you strike the metal...