Recent content by Legion81

For first year physics, I would recommend "Physics for Scientists and Engineers" by Serway and Jewett. It is a very readable text with plenty of examples and chapter summaries. As far as math goes, Thomas' Calculus is very good. It covers calculus of a single variable and multivariable...

fzero, I didn't even think of that! A free particle would have zero potential energy, so for L to be conserved it would still have to commute with the Hamiltonian, and that means L and P^2 must commute (2m factor is irrelevant). I thought for sure I was making a mistake somewhere since my mind...

Oh, I found one mistake but it still leads me to the same conclusion. The second equality should be plus, not minus: [A,BC] = [A,B]C+B[A,C]: \left[ \vec{L} , P^2 \right] = \left[ L^k , P_i P_i \right] = \left[ L^k , P_i \right] P_i + P_i \left[ L^k , P_i \right] = \left( - i \hbar...

I have been told that L and P^2 do not commute, but I don't see why. It seems like the commutator should be zero. \left[ \vec{L} , P^2 \right] = \left[ L^k , P_i P_i \right] = \left[ L_k , P_i \right] P_i - P_i \left[ L_k , P_i \right] = \left( - i \hbar \epsilon_{i}^{km} P_m \right)...

Ah! I should have thought of that. It's a problem in Griffith's EM chapter 12. They want the percent error using Galilean vs Einstein velocity addition for two things moving 5mph and 60mph. I guess it's to show this is a non-relativistic speed? Kind of ridiculous if you ask me. Thank you for...

I'm finding the percent error in a S.R. problem and getting a really small number. How can I find the exact percentage? This is the result that needs to be simplified: 6.7x10^(-16) / (1 + 6.7x10^(-16)) If I do an order of magnitude approximation, then the bottom becomes 1, but that will...

Thanks for the reply (and the latex sample!). It is acting on a vector A: \Gamma^{\tau}_{\alpha\nu} \frac{\partial A^{\alpha}}{\partial x^{\sigma}} - \Gamma^{\tau}_{\alpha\sigma} \frac{\partial A^{\alpha}}{\partial x^{\nu}} I've tried rewriting the partials as...

I would have to say mass does not create space. The 'curving' of spacetime is a description of the motion of an object near a gravitating body. It would follow a path given by the geodesic equation (which is a geodesic). I have never heard of space being a physical thing that can bend or distort...

No, time would not be infinite. It would be "normal" time (no time dilation). Just let r go to infinity in the equation and you will see that time is not changed.

Or more simply put: {alpha nu, tau}*d/dx^sigma - {alpha sigma, tau}*d/dx^nu = 0 How can I show this is true? Is there some way of writing this with the nu and sigma switched in one of the terms? Thanks.

I'm trying to work through getting the Riemann-Christoffel tensor using covariant differentiation and I don't see where two terms cancel. I have the correct result, plus these two terms: d/dx^(sigma) *{alpha nu, tau}*A^(alpha) and d/dx^(nu) *{alpha sigma, tau}*A^(alpha) Sorry, I couldn't...

I don't think humans have souls. If a soul was real, then you would have all types of questions like what is a soul made of, where does it come from, how long does it exist, what attaches it to a body, etc.. If you accept that a soul is imaginary, then your life is on equal ground to the...

I actually just found an easy way of showing it using projection operators. Thanks for the reply. Consider this question solved.

Helmholtz' Theorem starts with the two components in my original post and defines the divergence and curl as: div[V] = s(r) and curl[V] = c(r), where div[c(r)] = 0 But I can't find anything about how we can define a generic vector as two components: V = -grad[phi] + curl[A], where "phi" is...

I have to show that a generic vector can be decomposed into an irrotational and solenoidal component: V(r) = -Grad[phi(r)] + Curl[A(r)] I'm not sure how to start. Do I need to take the curl or div of V and use a vector identity? Any help would be greatly appreciated!