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--- classes:2009:fall:phys4101.001:q_a_1104 [2009/11/04 10:25] – x500_maxwe120
+++ classes:2009:fall:phys4101.001:q_a_1104 [2009/12/19 16:56] (current) – x500_sohnx020
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-===== Nov 04 (Wed)  =====
+===== Nov 04 (Wed) Laplacian in spherical coordinate, Legendre =====
 **Return to Q&A main page: [[Q_A]]**\\
 **Q&A for the previous lecture: [[Q_A_1102]]**\\
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 **Main class wiki page: ** [[home]]
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 ====Ekrpat 1144 12:50pm====
 A simple question about tuesday's discussion.  When solving for the eigenvector for the second and third eigenstate, I am getting
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+====Captain America 11/4 10:37====
+When dealing with the Hydrogen atom, we assume that the proton is a potential well for the electron.  We take electron to be a wave function and it is bound by a well, which is the proton.  Why can we take the well to be the proton?  If they are both attracting charges, should the equation work the same if the proton orbited the electron?  Would the proton then have a wave function itself, and the electron be a potential well?
+I'm also confused as to why we can call the proton a well, instead of calling it a wave function well, since in quantum mechanics all particles can be described as wave functions.  Anyone have any intuitive explanations for this?
+===prest121 11/4 12:30 ===
+When dealing with the hydrogen (or single-electron) atom, we make the assumption of a stationary nucleus.  This isn't entirely accurate, because the electron-proton system actually orbits about its center of mass.  However, since the proton is many orders of magnitude more massive than that of the electron, the center of mass of the system is very, very close to the proton.  So we take the proton to be the center of mass.
+I think this is what leads to us treating the proton as a 1/r potential well and the electron as a wave function/particle.  I think it is also related to the fact that we are primarily interested in the behavior of electrons in atoms (at the present time), not nucleons.
+===Pluto 4ever 11/5 11:11am===
+I also agree with this. We generally want to focus on the electron as opposed to the proton which we are assuming is stationary. That way in this ideal situation it becomes less complex to calculated the properties of the electron to some degree, such as such as probability of position and momentum, as well as energy and spin states.
+===Captain America 11/6 10:13am===
+But then why don't we treat the potential as a wavefunction?  Is it because the electrical charge that creates the potential doesn't behave as a wave?  I would think that the charge of the proton is distributed equally over the entire proton, and that the proton itself behaves as a wave, so the potential should not look like a pure harmonic oscillator, but a wavy harmonic oscillator instead.  Is what we do a simplification or am I over-complicating things?
+===David Hilbert's Hat 11/10 12:20pm===
+I tend to think that the effective wavefunction of a proton is very small relative to the potential it produces - for instance, whatever the effective "wavelength" of the proton's position is, it must be very small compared to how far away the coloumb potential reaches. I think finding a way to calculate these things might be difficult for any given proton (the free particle case is not easy, as we've seen) but intuitively you expect something with a charge on the order of 10^-19C to have much larger E&M properties than a quantum particle that has mass on the order of 10^-27 kg and is set at zero velocity. And very near the proton, when the quantum properties of each particle may come into play, is close to it - and the attraction between a proton and electron is repulsive, so it is unlikely that they are ever close to each other in the quantum sense.
+====Dark Helmet 11/05====
+Although i understand how to get them, what exactly is the physical interpretation of eigenstates and eigenvalues?  That still is confusing me a bit.
+=== Blackbox ===
+In quantum mechanics, operators correspond to observable variables, eigenvectors are also called eigenstates, and the eigenvalues of an operator represent those values of the corresponding variable that have non-zero probability of occurring. In other words, we can say some special wave functions are called eigenstates, and the multiples are called eigenvalues. I hope this helped.

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