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| classes:2009:fall:phys4101.001:q_a_1104 [2009/11/06 10:15] – jbarthel | 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]]**\\ | **Return to Q&A main page: [[Q_A]]**\\ |
| **Q&A for the previous lecture: [[Q_A_1102]]**\\ | **Q&A for the previous lecture: [[Q_A_1102]]**\\ |
| **Main class wiki page: ** [[home]] | **Main class wiki page: ** [[home]] |
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| ====Ekrpat 1144 12:50pm==== | ====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 | A simple question about tuesday's discussion. When solving for the eigenvector for the second and third eigenstate, I am getting |
| ===Captain America 11/6 10:13am=== | ===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? | 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? |
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| | ===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. |
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| ====Dark Helmet 11/05==== | ====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. | Although i understand how to get them, what exactly is the physical interpretation of eigenstates and eigenvalues? That still is confusing me a bit. |
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| | === 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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