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| classes:2009:fall:phys4101.001:q_a_0930 [2009/09/30 19:55] – x500_malmx026 | classes:2009:fall:phys4101.001:q_a_0930 [2009/10/05 20:06] (current) – yk |
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| === Anaximenes - 19:20 - 09/28/09 === | === Anaximenes - 19:20 - 09/28/09 === |
| As the professor said during class, <math>E=\(n + \frac{1}{2}\)\hbar\omega</math> starting from 0 makes it more clear what the ground state energy is than <math>E=\(n - \frac{1}{2}\)\hbar\omega</math> starting at n = 1. | As the professor said during class, <math>E=\(n + \frac{1}{2}\)\hbar\omega</math> starting from 0 makes it more clear what the ground state energy is than <math>E=\(n - \frac{1}{2}\)\hbar\omega</math> starting at n = 1. |
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| | ==== Blackbox - 10:10 - 10/04/09 ==== |
| | If it starts with n=0 for the harmonic oscillator, what about the ground state for infinite square well? |
| | As you know this <math>E_n = \frac{n^2\pi^2\hbar^2}{2ma^2}</math>, Why doesn't it begin with n=0? |
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| ====John Galt 18:19 9/28 (can you include date/time next time, John?)==== | ====John Galt 18:19 9/28 (can you include date/time next time, John?)==== |
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| I don't think anyone is suggesting that humanity give up on finding some reason for characteristics of particles to be indeterminate (maybe look into the source of the Schrodinger equation?), but (a) to make progress, we have to accept propositions at least as suppositions, and (b) no matter how much we ask "why are things like this?", eventually, the answer will have to be "they just are." Eventually, there won't be another answer. This isn't to suggest that we should stop searching; I mean that a statement that it looks like things "just are" has never stopped scientists from continuing to ask "why;" things have always seemed like they "just were." The fact that it seems like particles' location and momentum are indeterminate doesn't mean we won't keep exploring; people all over the world conduct research in the field of quantum mechanics. | I don't think anyone is suggesting that humanity give up on finding some reason for characteristics of particles to be indeterminate (maybe look into the source of the Schrodinger equation?), but (a) to make progress, we have to accept propositions at least as suppositions, and (b) no matter how much we ask "why are things like this?", eventually, the answer will have to be "they just are." Eventually, there won't be another answer. This isn't to suggest that we should stop searching; I mean that a statement that it looks like things "just are" has never stopped scientists from continuing to ask "why;" things have always seemed like they "just were." The fact that it seems like particles' location and momentum are indeterminate doesn't mean we won't keep exploring; people all over the world conduct research in the field of quantum mechanics. |
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| ====Andomeda==== | ====Andomeda 09/28 23:51==== |
| when it says "the quantum mechanical wave function travels at half the speed of the particle it is supposed to represent!" on page 60, I understand why the velocities are different but which one (classical velocity or quantum velocity) is the speed that can not be more than the speed of light? | when it says "the quantum mechanical wave function travels at half the speed of the particle it is supposed to represent!" on page 60, I understand why the velocities are different but which one (classical velocity or quantum velocity) is the speed that can not be more than the speed of light? |
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| ==== joh04684 - 8:14 - 9/29/09 ==== | ==== joh04684 - 8:14 - 9/29/09 ==== |
| Working through last-year's exam, I couldn't find any examples of when we'd done an infinite square well going from -a/2 to a/2, instead most of our examples (and in the book) go from 0 to L, so I was trying to derive the general <math>\psi_n(x)</math> solutions. Is it correct to use the form <math> \psi_n (x) = \sqrt{\frac{2}{a}}\sin{\frac{2n\pi}{a}x)</math>, and <math>E_n = \frac{2n^2\pi^2\hbar^2}{ma^2}</math>, where the only differences between a well from 0 to L and -a/2 to a/2 is inside the sin function (2nPi/a instead of nPi/a) and in energy (where you end up with a 2^2/a^2 instead of 1/L^2), but the normalization constant remains the same? Or is there some other simple intuitive way of formulating a solution to this? | Working through last-year's exam, I couldn't find any examples of when we'd done an infinite square well going from -a/2 to a/2, instead most of our examples (and in the book) go from 0 to L, so I was trying to derive the general <math>\psi_n(x)</math> solutions. Is it correct to use the form <math> \psi_n (x) = \sqrt{\frac{2}{a}}\sin{\frac{2n\pi}{a}x)</math>, and <math>E_n = \frac{2n^2\pi^2\hbar^2}{ma^2}</math>, where the only differences between a well from 0 to L and -a/2 to a/2 is inside the sin function (2nPi/a instead of nPi/a) and in energy (where you end up with a 2^2/a^2 instead of 1/L^2), but the normalization constant remains the same? Or is there some other simple intuitive way of formulating a solution to this? |
| ===Andromeda=== | ===Andromeda 09/29 20:42=== |
| i think the energy equation remains the same but the time independent schrodinger equation will either be <math>A_n\sin k_nx</math> for //n//=even integers or <math>B_n\cos k_nx</math> for //n//=odd integers due to the slightly different boundary condition. | i think the energy equation remains the same but the time independent schrodinger equation will either be <math>A_n\sin k_nx</math> for //n//=even integers or <math>B_n\cos k_nx</math> for //n//=odd integers due to the slightly different boundary condition. |
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| I also agree. You only need a single mass to analyze how quantum systems (e.g. atoms, light) work which applies to other masses of these systems. So whether it is the Schrodinger Equation or the Heisenberg Uncertainty Principle, you are more concerned about the behavior of the particle. | I also agree. You only need a single mass to analyze how quantum systems (e.g. atoms, light) work which applies to other masses of these systems. So whether it is the Schrodinger Equation or the Heisenberg Uncertainty Principle, you are more concerned about the behavior of the particle. |
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| ==== Malmx026 9/29 7:45pm ==== | ==== Malmx026 9/30 7:45pm ==== |
| My question is about the Pauli Exclusion Principle (a little more general). At what length do two fermions become close enough to say that they cannot have the same quantum state? More specifically this is shown in materials when the distance between fermions get close and the discrete band energies become spread out. Do the particles interact? | My question is about the Pauli Exclusion Principle (a little more general). At what length do two fermions become close enough to say that they cannot have the same quantum state? More specifically this is shown in materials when the distance between fermions get close and the discrete band energies become spread out. Do the particles interact? |
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| | ==== Malmx026 9/30 8:45pm ==== |
| | In problem 2.1 it is asked to show that imaginary energy is not possible because the wave function is not normalizable for all time, but if time is allowed to be imaginary then this isn't the case. Is imaginary time necessary to describe particles in any physical situation? Thanks |
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