Recent content by dragonlorder

I am no expert on this, but I think he's using a the property of integration \int^{b}_{a} f + \int^{c}_{b} f = \int^{c}_{a} f the intermediate terms are just writing out the [w(x)a\frac{du}{dx}]^{x^{e}_{i+1}}_{x^{e}_{i}} explicitly

Hmm yea, Thanks for the reply!

Thank you for the post I understand that F^* pull the form on x,y R^2 back to polar so the form would be expressed in polar R^2 as a pullback map acting on it F^* \omega while this seems pretty good, I noticed Lee wrote in his later chapter, \omega = dx \wedge dy = r dr \wedge d \theta kind...

I know this may sounds silly but I am confused consider this two form for example, by substitution, I get \omega = dx \wedge dy = d(rCos\theta)\wedge d(rSin\theta) = r dr \wedge d\theta also consider this smooth map F(x,y)=(rCos\theta,rSin\theta) then F^{*}\omega = rdr \wedge...

let Q be identity matrix, and A be a non symmetric matrix Q is positive definite but the product of those 3 is not hermitian

Ah, so Gauss Law indicates that the magnitude is the same if moves at constant velocity. But the direction of the field lines would be bent depends on which frame of reference you are in

Suppose you have a ring of charge and they can't move around. and you spin it, of course, we will have current. What about the electric field of the ring, the current indicates that there's electric field going around the ring.But Gauss's law kind of suggest, the electric field is the same as...

yea, later I found out any electron moving through 1V, must carry 1eV energy by definition, doesn't depend on which formula I use. In high speed, relativistic, of course

oh, so its defined in classical sense. I thought that since relativistic one was correct, so it might be the relativistic energy, but no. Thanks ~

Homework Statement I learned that by definition, one electron volt is the kinetic energy an electron would have moving between 1 voltage difference. if an electron moves between voltage of 1 million volts,then K = 1MeV, for example, but the problem is K is expressed in 1/2mv^2 or the...

thats exactly the problem I am having. how to modify that formula for the continuous situation

yea, but I feel weird having to integrate dF. The formula works for finite masses, but as the number goes infinite, it fails. But the formula for continuous rope should have the form similar to that of finite. that's why I feel weird to integrate dF.

Homework Statement I never thought I would have this kind of elementary problem consider a string closed-loop spinning around an axis, and its shape is a circle, I wanted to find the centripital force at each point. (uniform density is assumed). I have problem expressing the mass...

Ah! awww, thank you. Thanks everyone. That solves the problem ^ ^

the main reason that I am confused it that, I saw some solutions to some problems where you were given a wave function expressed in position space \psi (r,t) . And they measured the energy using the expectation value formula, <\psi|H|\psi>/<\psi|\psi> . How do they know the basis in position...