Recent content by hokhani

Thanks again for your help! To build on what I mentioned in post #6, the case I had in mind was specifically a rotation around the ##z## axis.

For rotation around the z axis ##p## and ##r## are orthogonal, or at least non orthogonal components don't contribute.

Also in quantum, the time evolution of an eigenstate appears as phase coefficient, and it seems that the phase change to be related to the origin of time.

In quantum mechanics phase change, as a coefficient ##e^{i\theta}##, would not change the quantum state. I would like to know whether we have such a concept for classical systems.

Here, it is not ##[x,p_x]## but we have something for example like ##[x,p_y]=0##.

So, for a constant ##L_z=m\hbar## we expect that getting far from the ##z-##axis the linear momentum decreases.

On the contrary, I think the particular case ##l=0## is more understandable from classical view. It describes the particle at rest. However, the quantum particle is not localized at a particular point. We can find it everywhere with the same probability.

Angular momentum as generator of rotation in defined by ##L=r\times p##. However, none of the angular momentum wave functions depends on the ##r##. They only depend on the angles.

As far as I know, photoelectric field requires a threshold frequency that under this frequency the effect can't be observed.

Could you please send the link to this insight?

If I understood correctly, you mean that intensity is independent of frequency. Isn't it?

Classical electromagnetic field can't explain photoelectric effect since at any frequency, increasing the intensity only increases the photon number and don't increase the wave amplitude (as was thought in classical waves). Since photons don't have enough energy they can not excite electrons...

In quantum mechanics, the uncertainty among the components of the angular momentum doesn't allow to find all the components together. However, when a quantum particle is confined to the ##xy-##plane, it seems that ##L_x## and ##L_y## are both zeros. How about the uncertainty here?

Is this wave function calculated by Hamiltonian?

Yes. Thanks all. Your comments resolved the ambiguity about internal energy and potential energy.