Recent content by ghc

p is a positive integer.

It is not a homework and I am not a student (and I never was a math student) but I can't prove it. So I will show what I can do : \frac{(n+1)^{-2p}}{n^{-2p}} = (\frac{n}{n+1})^{2p} \rightarrow 1 if n\rightarrow +\infty We can't conclude. \frac{(n+1)^{-2p}}{n^{-2p}} = (\frac{n+1}{n})^{-2p} =...

\sum_{n=2}^{+\infty}(\frac{1}{n})^{2p} where p \in N. Does this sum converge? How do we calcultate it? I am not very familiar with maths, so if there is some theorem that can used please tell it to me. Thank you.

If a phonon carry an energy, does this energy have a location? i.e. is there a probability density to find this energy on an atom? The energy of all atoms is everywhere on the crystal because they interact. Still oscillators have discrete energy levels? And do these energy levels have a...

Thank you. If oscillators are not coupled, each phonon will keep the same location which means that every oscillator will keep the same energy? And if oscillators are coupled the phonons will propagate through the crystal. In this case can we write a wave function which its modulus...

Question 1: If we consider that each atom in a cristal solid is a harmonic oscillator with the energy eigenvalues (n+1/2) \hbar \omega and if one oscillator has for example an energy (1+1/2) \hbar \omega, does this mean that there is a phonon located on this atom? Question 2: If this is true...

I'm not sure about my answer, that's why I will formulate it in a question: when a magnetic dipole with a magnetic moment \vec{\mu} is in a magnetic field \vec{B}, it has an energy E= -\vec{\mu}.\vec{B}. Now if \vec{B} is not uniform, there will be regions in space where the energy of the...

The infrared light and visible light are both described by photons and the photon's energy is E=h.f which f is the frequency. The only difference between visible light and infrared light is the value of this frequency f. The value of f depends on the frame from which we measure it. Thus the...

I think that the mass of the final object depends on the relative speed of the two objects before colliding, if both have the same rest mass.

Thank you JesseM! Coordinate acceleration is the derivative of the coordinate velocity with respect to coordinate time. Proper acceleration is the coordinate acceleration as seen in the inertial frame where the object is at rest in the moment when the derivative is taken, right? And the...

These two equations are in the book and tried to get one equation that relates the Riemann tensor to the metric and its derivatives by replacing all gamma's in formula (1) by their expression (done in formula (2)) then contracting the first and the third indices to express the Ricci tensor in...

The velocity is relative, that means we always need to precise the frame in which it is measured. The velocity of an object looks different if it is measured from different frames. However, acceleration has always the same "value" independently from which frame it is measured including the...

Thank you! I have another question: is there a formula in which the Riemann tensor is related only to the metric and its derivatives? if yes, can this equation give numerical solutions to EFE?

Accelaration is absolute. We can measure the absolute acceleration of A without knowing how B is moving. If A is accelerating we can feel a "gravitational field" in its proper frame.

Newton's third law says: if a body A exerts a force on a body B, the body B exerts a force on the body A and the two forces are opposite in direction and equal in magnetude. Relativity laws says that the interaction (forces) between A and B can't "travel" with a speed higher than c and a change...