L14.3 Particle in a constant magnetic field: Landau levels 

What is your point?

What is your point?

@@adamfattal9602 they're correcting the subtitles

I thought this is consistent with most textbooks (at least the ones I just read before coming to this video) which part did he get wrong can you specify ? I’m curious

​@@_HJ_K Glad someone is interested!. First, note that the wave function is of the form \phy(x,y)=f(x)g(y), where f(x) and g(y) are two functions depending of the variable "x" and "y" respectively. However, the first observation I'd like to make is pure mathematical. Note that if you write down the partial differential equation for the eigenvalue problem and attempt to solve it by proposing a general separable variable solution (that is, having the form \phy(x,y)=f(x)g(y)) hoping to recover Landau's solution, you won't be able to do so. The point of this first observation is that we are dealing with a NON-SEPARABLE VARIABLE partial differential equation. My second observation is about the physical properties of the system, just think about it a little bit, this solution has plane waves along the "x" direction, but, what is the main physical characteristic of a plane wave? The answer is the absence of potential energy. However, if one uses the Ehrenfest theorem to calculate an expression for the potential energy along the "x" coordinate, you'll figure out it is NOT conserved (and it shouldn't since we are expecting the particle to describe a circle, at least classically speaking). The point of this second observation is that we shouldn't have plane waves along a direction in which it's potential energy is not conserved. The third observation I'd make is that there is another conserved operator that he is ignoring, note that the operator "P_{y}+mwx", where w=qB/mc, also commutes with the Hamiltonian that is [P_{y}+mwx,H]=0. This analysis remains incomplete while he is not considering it. Finally, the degeneration of the system is not continuous but discrete and is given by the respective application of eigenfunction generators (the conserved operators).

No you, good Sir.