The discussion centers on the classical analog of the l=0 state in angular momentum, emphasizing that classical orbits cannot exist with zero angular momentum. It explains that in a non-quantized version of the Bohr model, the angular momentum L is defined as L = mvr, which becomes zero when the radius r approaches zero, indicating no orbit exists. The conversation also highlights the differences between classical mechanics and quantum mechanics, particularly in how particles behave in a centrosymmetric potential and the implications of the Dirac equation for relativistic corrections near the nucleus.
PREREQUISITESPhysics students, educators, and researchers interested in the intersection of classical and quantum mechanics, particularly in the context of angular momentum and atomic structure.
DrDu said:For angular momentum zero, in a centrosymmetric potential, the particle will move from -r to +r and back again along a line of constant angle phi. Hence it falls through the center. I do not see why this should be classically forbidden. If an obstacle (like a nucleus) happens to be in the center, the particle may or may not get reflected. In classical mechanics, the particle either gets completely reflected or not reflected at all, while in QM (like in the hydrogen atom) you usually observe a superposition of unreflected and reflected paths. Furthermore in QM, the angle phi is undetermined, which does not mean that it changes in time.