Discussion
This derivation treats x and y as slightly asymmetric. However, because of the symmetry of the system, there is no physical quantity which differentiates these coordinates. The same result could have been obtained with an appropriate exchange of x and y.
Additionally, the above derivation assumed an electron confined in the z-direction, which is a relevant experimental situation — found in two-dimensional electron gases, for instance. This assumption is not essential for the obtained results. If electrons are free to move along the z direction, the wave function acquires an additional multiplicative term ; the energy corresponding to this free motion, has to be added to E. This term fills the separation in energy of the different Landau levels, blurring the effect of the quantization. In any case, the motion in the x-y-plane, perpendicular to the magnetic field, is quantized.
Read more about this topic: Landau Quantization
Famous quotes containing the word discussion:
“Bigotry is the disease of ignorance, of morbid minds; enthusiasm of the free and buoyant. Education and free discussion are the antidotes of both.”
—Thomas Jefferson (1743–1826)
“This is certainly not the place for a discourse about what festivals are for. Discussions on this theme were plentiful during that phase of preparation and on the whole were fruitless. My experience is that discussion is fruitless. What sets forth and demonstrates is the sight of events in action, is living through these events and understanding them.”
—Doris Lessing (b. 1919)
“What chiefly distinguishes the daily press of the United States from the press of all other countries is not its lack of truthfulness or even its lack of dignity and honor, for these deficiencies are common to the newspapers everywhere, but its incurable fear of ideas, its constant effort to evade the discussion of fundamentals by translating all issues into a few elemental fears, its incessant reduction of all reflection to mere emotion. It is, in the true sense, never well-informed.”
—H.L. (Henry Lewis)