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| classes:2009:fall:phys4101.001:q_a_0925 [2009/09/25 10:47] – x500_szutz003 | classes:2009:fall:phys4101.001:q_a_0925 [2009/09/28 15:57] (current) – yk |
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| **Q&A for the previous lecture: [[Q_A_0923]]**\\ | |
| **Q&A for the next lecture: [[Q_A_0928]]** | |
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| ==== Anaximenes - 23:00 - 09/23/09 ==== | ==== Anaximenes - 23:00 - 09/23/09 ==== |
| ===chavez 9:22 9/25=== | ===chavez 9:22 9/25=== |
| I would start by writing <math>E_{0} = \hbar\omega/2</math> and then substitute this for <math>E</math> in the given equation and solve for x. Given this and the probability density function the problem should be pretty straight forward. | I would start by writing <math>E_{0} = \hbar\omega/2</math> and then substitute this for <math>E</math> in the given equation and solve for x. Given this and the probability density function the problem should be pretty straight forward. |
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| ==== Pluto 4ever 9/24 5:56PM ==== | ==== Pluto 4ever 9/24 5:56PM ==== |
| I was just wondering about the discussion problem. When we extend the barrier from L to 2L does it matter where the particle is along the ground path? | I was just wondering about the discussion problem. When we extend the barrier from L to 2L does it matter where the particle is along the ground path? |
| The barrier is assumed to move fast enough that the wave function is unable to respond immediately. Since the wave function is a description of the probability of where the particle may be, it does not matter where the particle is specifically. | The barrier is assumed to move fast enough that the wave function is unable to respond immediately. Since the wave function is a description of the probability of where the particle may be, it does not matter where the particle is specifically. |
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| == Spherical Chicken 9/25 10:30 == | === Spherical Chicken 9/25 10:30 === |
| Does it ever matter where the particle is on these scales? I thought the idea of making it a wave was that we don't really concern ourselves with where it is "really" because 1 it's on such as mall scale we can't exactly know, and 2, ... well we're approximating it with a wave... so aren't we saying the wall moves so fast the __wave__ can't simultaneously react? Am I misunderstanding all wave theory or isn't this where we approximate the particle //as// a wave (or a probability under the wave?), not as much a particle along a waves path? Perhaps my perception is really off... haha now I'd really like to know for sure that I'm either right or wrong... | Does it ever matter where the particle is on these scales? I thought the idea of making it a wave was that we don't really concern ourselves with where it is "really" because 1 it's on such as mall scale we can't exactly know, and 2, ... well we're approximating it with a wave... so aren't we saying the wall moves so fast the __wave__ can't simultaneously react? Am I misunderstanding all wave theory or isn't this where we approximate the particle //as// a wave (or a probability under the wave?), not as much a particle along a waves path? Perhaps my perception is really off... haha now I'd really like to know for sure that I'm either right or wrong... |
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| | === Ralph 9/25 10:55 === |
| | Hold on, when you ask where the particle is, are you asking about its wave function, its expectation value for position, or its "real position"? I had assumed that the original question was a question about where the wavefunction ended up being in the new 2L square well, rather than a question about the "actual" position of the particle (I thought this second interpretation was the classical way of thinking about the problem). But it does make me wonder: is the particle "interacting" with the walls of the potential well in the same way that we do when we "measure" something like position? I think I'm confusing myself now! |
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| | === Esquire 9/25 14:15 === |
| | It is my interpretation that you are rarely concerned where the particle exactly is, but rather the goal is to obtain the probability density function of the particle's position and work with expectation values. |
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| | === Anaximenes - 21:55 - 09/25/09 === |
| | The official answer (as seen on pages 3 and 4 in Griffiths) is that the probability distribution //is// the location of the particle. It does not describe where the particle might already be; the particle is at all of the points in the probability distribution (or, if you prefer, none of them until a measurement is made). You can talk about where you would //measure// the particle to be, but the answer to where it //is// can only be the probability distribution. I would suggest going back and reading pages 3-4 (or maybe all of chapter 1) again now that we've dealt with the problems a little. |
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| | For Ralph's question about whether the particle interact with the walls and whether any such interaction counts as measurement, I'm less sure, but I would say that we're assuming that the particle does not interact with the wall as the wall is moving and that there is no measurement involved. If that were not the case, the probability distribution would change. Whether this is a physically realistic situation, I don't know, but I'm dubious. I see it as more of a mathematical exercise to familiarize us with the math. |
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| | ==== Ralph 9/25 10:45 ==== |
| | I had assumed that the change in energy was the important part (rather than the specific initial position), and that the change in energy was directly related to the change in the dimensions of the infinite square well. It seems like the final state would be the same regardless of position because the change in energy is the same. The evolution of the probability distribution would be different (and the intervals of integration) , but the fundamental situation would remain the same. |
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| | ==== time to move on ==== |
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| | It's time to move on to the next Q_A: [[Q_A_0928]] |
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| | **Return to Q&A main page: [[Q_A]]**\\ |
| | **Q&A for the previous lecture: [[Q_A_0923]]**\\ |
| | **Q&A for the next lecture: [[Q_A_0928]]** |