Yes, phi is an eigenstate of (Lx^2 + Ly^2) if it is an eigenstate of Lz^2 and L^2, but in this case phi will not be an eigenstate of Lx nor Ly. So yes, Lx and Ly have a common set of eigenstates if you restrict yourself to the set of eigenstates of Lz, but that set is empty. Maybe I don't...
Great, thanks for the info Zenith.
Also, if the above refs don't include a formulation in which the only force on a particle is the pilot wave, I would still like to know if anyone knows of a ref for that.
Regarding question 1: As Zenith said, that article seemed to imply that gravity, ... act on the particle (mathematically through a potential V). Demystifier, do you know where I can look to find the formulations in which the only force on the particle is the pilot wave?
Regarding question 2...
I read a short high-level article about the pilot wave interpretation of quantum mechanics and I have some questions.
Is there a good way to formulate that theory so that the only force on a particle is from the pilot wave (inertia, gravity, EM, ... move/effect the wave which in turn...
If you use seemingly reasonable assumptions and then apply statistics to determine the behavior of a system of many particles (statistical mechanics) you will need state space to consist of "cells" of size hbar^3 in order for the resulting equations to match experimental results. For a gas of...
insightforge: from what others are saying, it sounds like you will not see an interference pattern when you look at the cases in which you didn't determine the which-path info. you only see an interference pattern when you look at a subset of those cases -- in terms of the diagram mentioned...
I wonder what the assumptions are in that theorem/corollary by Poincare? I ask because if you think of a 2D pendulum as an example, the bob of the pendulum can swing about any axis in a plane (say the "x-y plane"). If I start such a pendulum swinging about the x-axis only it will continue to...
But a difference of energies between members of the ensemble is allowed as well. Consider the example Pathria is using when explaining this stuff -- an ensemble of states with energy in the range [E - delta, E + delta] (i.e. the energy is not locked at a particular value). Any element of the...
Given a macro-state M of a system, let S denote the potion of the phase space that has the macro-state M.
A micro-canonical ensemble is one in which the probability of finding the micro-state in any part of S is equally likely (the density function is constant over S).
In Pathria's...
I went from computer science and math undergrad work to math and physics grad work to industry as an engineer. In my experience success (or at least promotions) in industry is based much more on your personality and how much you "play the game" while success in (science) classes is based more...
This is a little different subject, but is there a difference between (1) saying that objects are stationary but the distance between them is increasing and (2) objects are moving away from one another? I guess if the rate at which the distance changes itself changes then the difference is...
From what marcus said it sounds like GR implies either expansion or contraction, but it does not necessarily imply expansion at the rate predicted by redshift data on distant galaxies? True? If so, seems like there must be some other, more compelling reason why we believe the redshifts are due...
Are there any alternative theories/explanations of why light from distant galaxies is redshifted by an amount proportional to the distance away from us, other than the popular universal expansion explanation? Maybe some theory about light losing energy when traveling over such large distances...
what happens if we have a particle in a 1D box at the lowest energy level, and we shrink the box? i realize that it would need to get go to a higher energy level to continue to satisfy schrodinger's eqn in the smaller box. is that what happens? any links or explanation of the process?
thanks