Since you've only done Physics 1 & 2, you should work on strengthening your Classical Mechanics before jumping into Quantum. Perhaps, before getting Zettili for QM (here: http://tinyurl.com/zettiliqm [Broken] you could use Taylor's Classical Mechanics text (sophomore-junior level), found here...
After studying the methods of Lagrange and Hamilton for a bit I still find myself uneasy about the action. I don't even know how to define it other than the integral of the Lagrangian with respect to time:
$$I=\int_{t_1}^{t_2}\mathrm{d}t\, L(q,\dot{q},t)$$
Does the action have any...
Calculus 1 is all you need for K&K. Lagrangian and Hamiltonian mechanics are (unfortunately) not covered in K&K. A similar book in classical mechanics (which you should get after K&K or use it alongside it), Taylor, Classical Mechanics does include Lagrangian and Hamiltonian mechanics along with...
Once you finish (at least) the mechanics segment of Young and Freedman, you should go for this book: Kleppner and Kolenkow - An Introduction to Mechanics.
edit: Make sure you have a good grasp on calculus I material before getting this book, as it is used when solving problems and explaining...
Yes, that was the angle I meant.
That makes sense. I guess I'll have to be careful about my notation; I should have also included the step where the line integral transforms into an integral for ##d\theta##. Thanks for the help!
The radial component of the electric field cancels out at every point due to the symmetry of the circle and the fact that the electric field arises from a line charge. This leaves us with the z component of the electric field, which can be calculated by carrying out the following integral (is it...
Homework Statement
Find the electric field a distance z above the center of a circular loop of radius r that carries a uniform line charge λ.
Homework Equations
$$E=E_r\hat{r}+E_z\hat{z}$$
$$E_r=\frac{\lambda}{4\pi\epsilon_0}\int_0^r\frac{1}{\mathcal{R}^2}\sin{\theta}\,dr$$...
Apparently it seems like a convention.
Correct me if I'm wrong but Landau shows that ##L=L'## under Galilean transformations. Did you want me to explain how? Unless that's the case, then I guess him going to the action is probably a convention, a way to prove this invariance. I think if you...
I think its just another way of proving Galilean invariance (I'm not very familiar with the Galilean invariance of the Lagrangian). Do you mind showing me how they go about proving this (the part where they go to the action)?
I might be able to use that information and relate it to the value of...
If you haven't read an intermediate text before L&L (eg. Taylor, Marion and Thornton, etc) then I highly recommend going through https://www.amazon.com/dp/189138922X/?tag=pfamazon01-20 before venturing into Landau or Goldstein or anything at that level.
Yes, conserved quantities arise from invariances within the Lagrangian. For example, if the Lagrangian does not depend on time, the Hamiltonian (total energy of the system) is conserved.
Basically what he's saying is that if you shift all of the particles in the system to a new position:
$$r_{\alpha}\to r_{\alpha}+\epsilon$$
and find that the Lagrangian stays the same, then it is demonstrating translational invariance. As a consequence of this translational invariance, momentum...
I admit I haven't read French but from all the reviews it seems quite decent. If OP can not / does not want to pay for HRW or YF he / she might as well pick up French.
I'll jump ahead and give you some introductory physics books just in case you want to give them a look. Once you're done with these, you can move up to upper-level texts:
Assuming you've done single variable calculus (and even if you haven't, these books don't really include calc much)...
I agree; Young and Freedman is quite verbose. You said you know calculus so you should get this book (even if it isn't used that much). Once you work through chapters 1 - 13, you should get Kleppner and Kolenkow, which uses calculus much more and is a text used by advanced freshmen and...
I'll give you a brief list of mechanics texts:
Harvard - Introduction to Classical Mechanics by David Morin: very difficult; used by honors physics students.
MIT - Kleppner and Kolenkow - An Introduction to Mechanics; the book I bought for self-study; used by honors physics students. It's not...
Integrating by parts twice (first using ## x^2\lambda=u## and the second term as dv), I get:
$$\frac{x^2e^{-2\lambda|x|}}{2}+\frac{xe^{-2\lambda|x|}}{2\lambda}-\frac{e^{-2\lambda|x|}}{4\lambda^2}$$
I see my mistake. Also, how does the function being odd or even affect the integral? I'm a self learner so I'm not surprised at the fact that my knowledge is fragmented.
I'm guessing this means that the expectation value is 0. How can this be?