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:
“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)
“It was heady stuff, recognizing ourselves as an oppressed class, but the level of discussion was poor. We explained systemic discrimination, and men looked prettily confused and said: “But, I like women.””
—Jane O’Reilly, U.S. feminist and humorist. The Girl I Left Behind, ch. 2 (1980)
“The whole land seems aroused to discussion on the province of woman, and I am glad of it. We are willing to bear the brunt of the storm, if we can only be the means of making a break in that wall of public opinion which lies right in the way of woman’s rights, true dignity, honor and usefulness.”
—Angelina Grimké (1805–1879)