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)
“We cannot set aside an hour for discussion with our children and hope that it will be a time of deep encounter. The special moments of intimacy are more likely to happen while baking a cake together, or playing hide and seek, or just sitting in the waiting room of the orthodontist.”
—Neil Kurshan (20th century)
“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)