Hello i am doing a masters in nanosciences and nanotechnology ,, and i have a problem about the difference between the Landau levels and energy levels in quantum mechanics . since they are both the same to me ?

Thanks

 

My knowledge on this is limited by practical application using the quantum Hall effect so don't take this as gospel.

I think the main difference is: In the presence of a magnetic field, energy levels become equally spaced or ordered (gap between each level proportional to the magnetic field B). This spacing of energy levels is called Landau levels. The quantum levels of an electron in constant magnetic field (Landau levels)
Classical

Quantum

 

To expound a little more upon what @nsaspook said, Landau levels are, effectively, the energy levels of "free" electrons in a magnetic field, while "traditional" energy levels arise from electrons trapped in other kinds of potential wells. As it turns out, even these "free" electrons, when trapped in cyclotron-like orbits, exhibit quantization of energy levels. It somewhat makes sense, as you can, very roughly speaking, consider these magnetic fields to be a "different" kind of "potential well," and should, as such, exhibit energy level quantization.
Hopefully, that's sufficiently not-vague-enough to answer your question. Wikipedia has a semi-decent explanation on them, too ("Landau Quantization").