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:
“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)
“If the abstract rights of man will bear discussion and explanation, those of women, by a parity of reasoning, will not shrink from the same test: though a different opinion prevails in this country.”
—Mary Wollstonecraft (17591797)
“Americans, unhappily, have the most remarkable ability to alchemize all bitter truths into an innocuous but piquant confection and to transform their moral contradictions, or public discussion of such contradictions, into a proud decoration, such as are given for heroism on the battle field.”
—James Baldwin (19241987)