# Recent content by Legion81

1. ### I want to self teach physics

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...
2. ### Angular momentum commutator

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...
3. ### Angular momentum commutator

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...
4. ### Angular momentum commutator

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)...
5. ### Simplifying expression

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...
6. ### Simplifying expression

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...
7. ### Riemann-Christoffel tensor

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...
8. ### Mass creates Volumetric Space

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...
9. ### Infinite speed of time

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.
10. ### Riemann-Christoffel tensor

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.
11. ### Riemann-Christoffel tensor

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...
12. ### That's a soul?

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...
13. ### Would you put off graduating?

I have two options right now and I would like to hear what you would do in this situation. I don't have any research experience to put on a grad school application. If I take the GRE this fall, I will just be starting QM, so I probably won't be able to solve many of the QM questions on the...
14. ### Vector decomposition (Helmholtz)

I actually just found an easy way of showing it using projection operators. Thanks for the reply. Consider this question solved.
15. ### Vector decomposition (Helmholtz)

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...