Recent content by Observable

Though it´s not appropriate to say ¨the velocity¨ of the electrons in an atom, there´s still semi-classical analog: probability flow density. Also, you can mimic the conception of velocity as p/m, where p is the momentum operator, take the expectation value of p/m, you can get a semi-classical...

clearly not.

I don´t understand your position clearly. But I think there´s thousands of ways for the ´lost energy´ to go: photons, internal energy for gas particles,etc. Otherwise, the increase of kinetic energy should be equal to the decrease of potential energy.

Actually,the exact formulas for Ex,Ey,Ez are the same as separable Helmholtz eqations in Cartesian coordinates. The Gaussian packet(beam) form is just a kind of B.C. You can simply superpose plane waves(in coordinate) to get a Gaussian shape. In this sense, kx,ky are generally non-zero,so Ez...

There´s an assertion that the electric field depends only on Vector potential in radiation region. But I couldn´t see clearly why the contribution of scalar potential could be comparatively ignored. Could anyone give me some explanations? Thanks!

As the example you posted, the main point of it is that if you are going to buy cheap stuffs, you'll have more choices(more combinations) to distribute your finite money, while for the expensive ones, you'll have much less choices. More choices means larger probability. Thus higher intensity.

I think those applications are actually treated by WKB approximation, so comes the linear potential

convert it into potential Constant force can be treated as linear potential. Then you can solve it sectionally. A similar problem has been investigated: V(x)=ABS(x). The solution to this potential is just Airy functions. But it doesn't have as much practical value as the ones show up in QM...