Recent content by rays

Demystifier, Thank you. I think I get it this time. Please correct me if I am wrong: Based on what you said and some research I believe that the free particle wave function (exp(ipx)) is fundamentally flawed since it says <x>(t) = const. With a Gaussian wave packet (which is not an energy...

Bill_K, Agree with your post. But the ih<dA/dt> = <[A,H]> is where the Ehrenfest theorem comes from. In Sakurai 2nd ed, Page 73, it was proved that for a stationary state, expectation value of any observavle (regardless of whether it commutes with H) is independent of time. The proof is...

I've just found out that there is a proof of x(t) = x(0) + p(0)t/m for a stationary state free particle in Sakurai (2nd ed. Eq. 2.2.27). But for any stationary state <x> = const at all times. rays

Thanks, Demystifier. I can understand the difficulty with the free particle wave function. But even qualitatively, the Ehrenfest theorem (a time-dependent <x> makes sense to me) contradicts what the free particle wave function says (<x> = 0 at all times). if Ehrenfest theorem does not apply...

for a stationary state (energy eigenstate) psi(x,t)=u(x)exp(-iEt/h) <A> = integral of psi* A psi dx. The time dependence exponentials cancel each other. <A> has to be time-independent regardless of its commutation properties with the Hamiltonian (there is a proof of it in Sakurai, 2nd ed...

For a free particle stationary state, one would expect the expectation values are constants, for example, <x> (t) = 0. From its one dimensional wave function psi(x,t)= exp(ipx/h-iEt/h)/L^1/2, <x> is undefinied (or zero since x has odd parity). How does one reconcile the above with Ehrenfest's...

Thanks again. In the rotating frame of thomas precession, the B field from the non rotating frame in its entirety is used to describe the motion in the rotating frame. This seems in contradiction to the treatment of other scenarios. For example, in nuclear magnetic resonance, when one...

Bill_K, Thank you! I understand that the actual B field is not changed during Larmor precession. However, the equaiton of motion in the rotating frame should read dL(angular momentum)/dt = gamma*L x (B-B') while B' is the fictitious magnetic field. In Thomas precession, one writes...

According to Larmor's theorem, the magnetic field seen by a rotating frame is changed. In a frame that rotates at the Larmor frequency, the magnetic field appears nonexistent. In the treatment of thomas precession, the magnetic field in the instantaneous resting frame (which is rotating to...

mfb, Thank you for the quick reply! In classical eletromagnetic theory, if the incident EM wave is linearly polarized (no angular momentum) and it is scattered by a fixed spherical perfect conductor, then can the scattered EM wave be elliptically polarized? rays

If the incident radiation is linearly polarized can the scattered radiation be circularly or elliptically polarized? If the scatter is a lossless dielectric the scattered radiation is not elliptically polarized. How about if the scatter is conducting? if the scattered radiation is elliptically...