Recent content by vector

Here's what my prof says: "Define F_{mean} to be the mean force, F_close to be the force on the side of the Earth closer to the moon, and F_far to be the force on the side of the Earth furthest away from the moon. On the closer side the net force is F_close - F_mean > 0 On the further side the...

vanhees71, thank you for your detailed post. From your post, it appears that Classical Mechanics is not extensively applied in GR, and that GR is quite abstract. Which would be good for me, because I seem to lack some intuition for Classical Mechanics, and do prefer more abstract courses, like QM.

If that's the case, it seems that I'll have to take Differential Geometry instead. I was really looking forward to learning GR, including the Differential Geometry part of it, but I have a bit of a trouble with Classical Mechanics. Actually, a course in Quantum Theory in my school also has...

I'm currently taking a course in Theoretical Mechanics, which is a prerequisite to General Relativity, which I'm very much looking forward to taking. However, I'm not that good in mechanics, and Real Analysis seems to be more straightforward than even the first course in Mechanics. I'm quite...

Thanks, I managed to do the question. The Bohr frequency turned out to be ##\frac{E_2-E_1}{\hbar}##, if I was correct.

I've calculated the eigenvector corresponding to ##a_1## to be ##1/\sqrt{2} (1, 1)##, so I think ##\lvert \psi(0) \rangle = 1/\sqrt{2} ( \lvert E_1 \rangle + \lvert E_2 \rangle)##. So the expectation value appears to be ##1/2 (E_1+E_2)##. But how can we read the Bohr frequency from here?

Homework Statement Consider a two-state system with a Hamiltonian defined as \begin{bmatrix} E_1 &0 \\ 0 & E_2 \end{bmatrix} Another observable, ##A##, is given (in the same basis) by \begin{bmatrix} 0 &a \\ a & 0 \end{bmatrix} where ##a\in\mathbb{R}^+##. The initial state of the system...

I have now solved this problem. I had actually misinterpreted the problem, as I thought it was about relativistic waves rather than water waves :)

Thanks. So, the ##\frac{ET^2}{\rho_0}## should be raised to the power of 1/5, shouldn't it?

Sorry, I meant ##L^5##. So then the expression is not quite homogeneous. Namely, the units of ##R## are ##L##, but the units of ##\frac{ET^2}{\rho_0}## are ##L^5##. Am I correct?

Thanks. But do you think the expression given in the problem statement is correct at all? The problem is that ##R## has units of ##L##, but ##\frac{Et^2}{\rho_0}## has units of ##L^{-5}##.

Homework Statement :[/B] An atomic explosion can be approximated as the release of a large amount of energy ##E## from a point source. The explosion results in an expanding spherical fireball bounded by powerful shock wave. Let ##R## be the radius of the shock wave and assume that...

Stumbled upon this problem lately. Maybe someone could help me clarify some subtleties I do not see? 1. Consider the propagation speed ##c## of periodic surface of gravity waves with wavelength ##\lambda## and amplitude ##a## in water of depth ##H##. Let ##\rho_{a}## and ##\rho_{w}## be the...

Adithyan, I'm probably missing some important point. Let me explain. Here's the solution in the study guide: Case one, x1=0. The youngest child gets zero candies: x1+x2+x3+x4+x5+x6=20. Now, they say, in this case we have C(20+6-1, 20) = 53,130. But here's my view: in this equation, we...

Hello Everyone, There is one interesting exercise in which it is asked to solve the following problem: In how many ways can we distribute 20 candies among 6 children so that the youngest gets at most 2 candies? This is my version of the solution: Case 1: youngest child gets no...