I'm studying the Landau quantization of free electron systems and a question comes to my mind when I arrive to the degeneracy of the levels. This is given by the following expression:
Where $H$ is the magnetic field and $L^2$ is the area of the system in the direction perpendicular to the magnetic field.
As we can see, this expression does not depend on the energy level. How is this possible? I mean, following my intuition, when we turn on the magnetic field, all the levels being $ħ\omega_c$ around a Landau level, collapse into this Landau level, so at the end, the number of states in a particular level should increase as we go to higher Landau levels, as well as the degeneracy, since at higher energies in the free electron model the number of available states increases. Am I wrong about this idea? I guess intuition can fail when we talk about these complex phenomena.