timo

Intuitively: A force (vector) acting on the ion can be decomposed into two parts: A part parallel to the velocity that pulls the particle to go faster or slower and a perpendicular part that modified the direction. That is of course not a convincing argument' date=' but perhaps gives you an idea what happens. Physically: The force [math'] \vec F = q \vec v \times \vec B [/math] is the change of momentum [math] \vec p = m \vec v [/math] over time: [math] \frac{d\vec p}{dt} = \vec F[/math]. So the change in the square of the momentum is [math] \frac{d(\vec p \cdot \vec p)}{dt} = \vec p \cdot \frac{d\vec p}{dt} + \frac{d\vec p}{dt} \cdot \vec p = 2 \vec p \cdot \frac{d\vec p}{dt} = 2 \vec p \cdot ( q \vec v \times \vec B ) = \frac{2q}{m} \underbrace{\vec p \cdot ( \vec p \times \vec B )}_{=0} = 0[/math]. In other words: [math]\vec p \cdot \vec p = |\vec p|^2 [/math] is the same for all times. Then so is [math]|\vec p|[/math], of course. Then so is [math] |\vec p / m | = |\vec v| [/math], the speed. EDIT: I think Swansont's argument via work is more mainstream than my calculation so it is possibly easier to understand.

Or how the Large Hadron Collider works. The formula you are looking for is the Lorentz force. Note however, that this force due to a magnetic field will always be perpendicular to the current velocity. In effect (and first approximation) you will only change the direction of your ions, not their speed.

Try plugging into the definition for it. It must be defined as something, after all.

I think unless you have specific questions you're better off googling for an intro text, say for "introduction tensors", read it and ask here if you have specific questions. Someone here might be willing to give you an introduction here without you having asked a specific question. But it will certainly not reach the quality of stuff you find using Google.

Sadly, Hawking can't play for the physicists team in his preferred role as a goal keeper ... the national team needs him.

I would start trying subsequent simple coordinate transformations: 1) A rotation matrix A that rotates the position of the man into the x-y plane. 2) A rotation matrix B (rot around the z-axis) that moves the man on x=1, y=0 (or however you label say your north pole). 3) A rotation matrix C (around the x-axis in my proposal) that rotates the forward direction to e.g. (0,1,0). 4) You know can now apply your step forward (in my example he will walk counter-clockwise in a circle in the x-y plane). 5) After that, you probably want to transform your coordinates back to the original coordinate system, i.e. undo steps 3, 2 and 1 in that order. That is done with the matrix [math]A^{-1}B^{-1}C^{-1}[/math], the exponent -1 denoting the inverse, in case you are not familiar with matrices (you'll probably need a lot more help in this case, then). Hint: Denoting the stepping (in the rotated intermediate coordinate system) symbolically by X (in fact it is just another rotation matrix so you can actually write it as a matrix) the mathematical expression for the step from the old coordinates x to the new coordinates y is [math] y = \underbrace{A^{-1}B^{-1}C^{-1}}_{=T^{-1}} \ X \ \underbrace{CBA}_{=:T} x [/math]. By construction, you already know what XCBAx will be (because the matrices were constructed to get that result). Let's call that z. So the problem you have to solve is finding the inverse of CBA (or their individual inverses) and then applying it on z. There might be a more intuitive way. Since the matrices in question are all rotation matrices around one of the main axes it's quite likely that writing down the mess analytically can lead to drastic simplifications (if you have access to a computer algebra system or like doing math then you could try that). But it should work in principle. EDIT: Be aware that the proposal above does not take into account the way you expressed x-, y- and z-coordiante as a function of two angles (was too lazy). So a different order of rotations might suit you better. But I hope you get the idea. Thank you for a non-homework, non-"I proved Einstein/Gödel/Fermat/God/yourmotheronapogostick wrong" thread.

The question is not asking for equal velocities upon impact but for equal speeds, i.e. magnitudes of velocities. You are of course be correct about different velocities: the horizontal part of the velocity is differs when thrown and not change during the flight. Note that the question is very homework-like, so I think you should be a bit reluctant to discuss details of a solution until MDJH has presented a solution or at least a week or so has passed.

Also note that the Higgs boson is associated with a mechanism that creates mass (-terms), not a mechanism that creates matter.

I cannot give a good advice but there is a problem with most of these "help me decide on a scientific career path" that also applies here and that you probably should be aware of: You do know next to nothing about your stated field of interest (at least the physics part). You are interested in your imagination of the fields, not the field itself. Granted, there is little you can do about that but you should at least be aware of it and make your decisions on a broader level like how you'd like your work-routine to look like. For example: I do computer simulations involving random events to some extent. The majority of my time is spent on programming the simulation and analyzing the results. Whether the simulation I set up is about - the generation of artificial black holes in particle colliders (particle physics), - the formation of galaxies under the influence of various types of dark matter (atrophysics), - the transition of water molecules from a liquid to a gaseous state (soft-matter physics), - the diffusion of defects in a crystal structure (solid state physics), - or people trying to escape a burning building (non-linear dynamics) is pretty irrelevant for most of my work. And I could see myself being interested in all of these examples so it wouldn't really matter which simulation I actually do write (except that I prefer writing my own code over working in a collaboration). And if you're looking for something to impress women then go for firefighter or paramedic

Guess not realizing that explains why I am on place 20

16 out of 20 people in my betting group (for a win by Chile, not necessarily the exact result).

It's surprising how everyone jumps on it, though. Despite its total irrelevance for the thread.

There's a [math]\pi[/math] missing which reflects the symmetry of the universe. It was mentioned in some forgotten notes of Tesla.

It helps adjusting the response. I certainly think there's a difference talking about say "is the moon possibly held in orbit by magnetism?" with a 10 year-old kid, a young non-science student, a 50 year-old engineer or a physics PhD student (though the last two cases would probably leave me speechless). I do appreciate that Klaplunk did introduce him-/herself.

1) This is homework so you should probably have posted the question in the homework section. 2) There you might have read that it is not the idea of this forum to give solutions but only to help the people at finding the solution themselves. 3) Also, you might have read that you should state what you already tried and did yourself. 3a) You are given a function x(t)=... for the displacement x for each time t. Do you think you are able to find the displacement x at some given time t=2 from that? 3b) How are velocity and acceleration related to the displacement/position? Start with the velocity: What is the definition of velocity? Can you apply this definition to the only information you were given, the function x(t)=.... ? Btw: The greek letter [math]\, \pi[/math] is written "pi", not "pie". But that does not matter for your question, of course.

I have no idea what you are trying to tell me there. I did not talk about a composite system in any place. I do not necessarily use mainstream labels in case that irritated you. That's why I said what the respective variables stand for. It's the physics that matters, not the letters used to describe it. Are you asking a question in this thread or are you trying to teach something to us?

The energy of a magnetic dipole [math]\vec m[/math](consider the spin as a magnetic dipole) in a magnetic field [math] \vec B [/math] is proportional to [math] - \vec m \cdot \vec B[/math] (such that energy is minimized for parallel orientation and maximized for anti-parallel one). From that, constructing the Hamiltonian should be straightforward (looking up the constants, replacing observables with operators, be happy). Depending on what you want to do with your Hamiltonian, a smart choice of coordinate system might be a good idea. Remark: Iirc might be a rather unexpected factor of 2 somewhere in the transition from the spin to the magnetic moment, but you'll probably see that yourself.

Run less programs at a time, switch to programs that require less memory themselves. It would probably be better if you described what you actually want to do (and why), what kind of computer you are talking about, possibly what operating system you are using, ... .

In that case ideas that come to my mind spontaneously are (in that order): (1) Consider doing something else than physics in your free time, e.g. some sports activity. You should already do physics quite a lot. Many people consider it a good idea doing something entirely different to balance their live (and maybe even have social contact with normal people). (2) Actually take university courses beyond the level proposed for 2nd semester. While it might be interesting for you to read books beyond what you are currently taught it is of pretty little help for you if you have to take courses in that subject (in this case QM) later on in any case and get bored, then. I think it's better to actually take the course and pass the exam and finish your course early and get to the more specialized and more important topics sooner. Maybe talk to the lecturers if attending higher-semester courses is problematic in your university. I don't expect anyone to have a problem with an interested lower semester attending their lecture. (3) Reading the books that are proposed for future classes seems a better idea than reading random books. (4) I would not advice to read several books on the same topic but rather browse through different fields to get an overview and see what interests you. (5) If you really want to read another QM book then I'd go to the library, have a look at a few of the books and chose the one which is readable (of course) and contains the most topics naturally extending what you already learned. I know neither Griffith nor Sakkurai but I would expect that books called "Introduction to QM" and "Modern QM" contain pretty much the same content so reading Sakkurai might become a bit boring (though I might be wrong considering the books seem to be used for different courses - see (3) ).

"Getting a life" is what comes to my mind, although that probably sounds a bit offensive (it's not; in reality I envy people who have the patience to work through a physics textbook for their patience). But seriously: How is the average sfn forum participant supposed to know that? It strongly depends on who you are, what you are doing and where you want to go. If you are a physics student then the obvious next step seems to be "take the exam". If you are a pupil who is interested in physics and reads books that are way more advanced than the school stuff -and interested in physics- then I'd suggest looking if the local university accepts pupils in a few lectures (oh, and for giving hints on that it would help to know where you are from - not everyone here is from Spain, after all). If you are a retired engineer interested in modern physics then perhaps you should state what, after working through Giffith, sems to sound the most interesting to you to investigate next.

What is that text supposed to be? It certainly doesn't make me any more or less angry (or amused) than the average "physicists are brainwashed from university and hence cannot acknowledge my great theory of 'everything consists of pure energy'"-post on sfn. That is unless there is a reason to take this text seriously.

Well, I was serious about the idea with the coin, in case that wasn't clear. With coins, the distribution is the binomial distribution which excel should be able to handle (and coins are still valid for showing the effect of entropy).

I don't know a solution to your problem out of my head but there is one thing that comes to my mind:

What does k stand for, what it is value, how did you get this value? Note that usually the force is written as F = -k*displacement, not F=-(k/4)*displacement. But using k/4 consistently should still work fine in your case. EDIT: Got the constant on the k wrong myself. should be fine, now.

Silly me forgot to save the message before posting and was logged out. In short: - Don't fall into the trap thinking you had a good grasp of QM. There is some intermediate plateau in learning QM (the chemists' plateau ). You are blocking your progress by mistaking it for the peak. - Do exercises. Not only solve the problems but reflect on the solutions after you got there and try to figure out in hindsight why obviously this way to solve the problem was one that lead to success. - Form a learning group with others. Having people to discuss ansatz and result can be very helpful, I think. - Have a look at the book by Schwabl.