Thanks to everybody for your comments, it helped me a lot. I finally understand where my confusion was coming from; I got stuck in an incorrect idea. Now it is clear. Position really does not commute with the Hamiltonian in hydrogen atom. And also I understand better the difference between...
Thank you for the answer. So it was no surprise that my commutator turned up to be zero, because I put x time independent, and that ensured it commutes with the Hamiltonian. But in general the position operator does not have to be time independent (in Heisenberg picture) and does not need to...
I was thinking that \partial_{t}x=0, because \hat{x}=x does not seem to depend on time. The operator \hat{x} is just multiplication by the coordinate x and it does not change in time, so \partial_{t}x should be zero. It would be non-zero only if \hat{x}=x(t). But I'm probably missing something.
The problem is that I'm having difficulties finding the correct commutator between the position and the Hamiltonian. Usually it is written that these 2 operators do not commute. See for example here on the second page, expression (306) and (307).
But when I calculate the commutator between...
The time dependent Schrödinger equation is:
i\hbar\partial_{t}\Psi=\hat{H}\Psi
Does it mean that the operator i\hbar\partial_{t} has the same eigenstates and eigenvalues as any Hamiltonian?
You can read more about QED here.
To describe electromagnetic field QED is using the electromagnetic four-potential Aμ. The classical electric and magnetic fields can be calculated from the four-potential Aμ: see for example here (page 332 onwards).
Photon is an excitation of the quantized...
Derivative of a field can be negative and it often is negative. If it were always positive (or zero), the field value would be always and forever growing (or not changing).
It is more difficult to see the Higgs particle in the noise. Identifying the top quark is easier than identifying the Higgs. So you need a collider with higher luminosity, which is the LHC.
Regarding the Higgs being "found" at the Tevatron: I don't think they had 5 sigma significance to declare...
The photons of cosmic background radiation lose their energy continuously due to continuous expansion of space. No scattering off gravitons is involved.
I'm not sure I understand why you need an operator to fill your box with photons.
1. Photon frequency is not changed in double slit experiment, nor during reflection.
2. Particles are entangled with other particles, if they interacted.
1. Lorentz transformation is describing the relations between measurements of 2 observers. These observers can measure various elapsed times or distances between the same events, if these observers are in relative motion. It is a relativistic transformation.
2. Galilean transformation does...
1. Spherical wavefronts change into plane wavefronts at infinity, because the radius of the sphere grows with the distance. A sphere with infinite radius has zero curvature: it is a plane.
2. This is caused by diffraction.
I'm still not sure I understand your question. Wavelength is just the distance between 2 crests. There is no deeper mystery behind that and it's not possible to explain it more clearly. Maybe showing the image.
Or are you asking about the wavelength of an electron? Well, electrons are...
The distance does not affect the frequency. When you increase the distance from the sound source, the intensity is dropping. Intensity is power per unit area. When you are farther away, the acousting power from the source is spread over larger surface (sphere with the radius equal to your...