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| classes:2009:fall:phys4101.001:lec_notes_0909 [2009/09/09 22:53] – created yk | classes:2009:fall:phys4101.001:lec_notes_0909 [2009/09/23 22:42] (current) – yk |
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| ===== Sept 9 (Wed) ===== | ===== Sept 9 (Wed) Broad overview of Chap 1===== |
| **Responsible party: East End, Spherical Chicken** | **Responsible party: East End, Spherical Chicken** |
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| | **To go back to the lecture note list, click [[lec_notes]]**\\ |
| === Okay, editing now. (7:00 pm Friday) Check back later. --East End === | **To go to the next lecture note, click [[lec_notes_0911]]** |
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| === Requisite introductory material === | === Requisite introductory material === |
| Also, remembering that <//f(x)//> is given as <math><f(x)> =\int f(x)P(x)dx</math> //(eq. 1.18)//, we can easily derive formulas for <//x<sup>2</sup>//>, etc. | Also, remembering that <//f(x)//> is given as <math><f(x)> =\int f(x)P(x)dx</math> //(eq. 1.18)//, we can easily derive formulas for <//x<sup>2</sup>//>, etc. |
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| We also were given that the standard deviation is given by <math>\sigma=\Sigma(x_n - \bar{x})^2P_n=\Sigma x_n^2P_n - \bar{x}^2</math> for the discrete case, and <math>\sigma=\int(x-\bar{x})^2P(x)dx=\int x^2P(x)dx - \bar{x}^2</math>. | We also were given that the standard deviation is given by <math>\sigma^2=\Sigma(x_n - \bar{x})^2P_n=\Sigma x_n^2P_n - \bar{x}^2</math> for the discrete case, and <math>\sigma^2=\int(x-\bar{x})^2P(x)dx=\int x^2P(x)dx - \bar{x}^2</math>. |
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| The steps going from the centers to the left hand sides of those equations, to me, are "wonderful tricks," and I am going to be asking about this in the Q&A if nobody else has. | The steps going from the centers to the left hand sides of those equations, to me, are "wonderful tricks," and I am going to be asking about this in the Q&A if nobody else has. |
| The answer to the second question was a little more interesting. Because waves are interesting. Waves can interfere with each other. Most of the time we add two things together and they strictly reinforce. Waves can cancel each other out or reinforce each other. So can the wave functions for particles. Or at least they would, if the particles involved didn't follow the Pauli exclusion principle. | The answer to the second question was a little more interesting. Because waves are interesting. Waves can interfere with each other. Most of the time we add two things together and they strictly reinforce. Waves can cancel each other out or reinforce each other. So can the wave functions for particles. Or at least they would, if the particles involved didn't follow the Pauli exclusion principle. |
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| **Yuichi** - This seems to be a wonderful start and example of pretty complete note on the materials we discussed today. There may be a few things someone can add, but if the notes for the rest of the semester continue this trend, I feel we will have great lecture notes for this class. Thank you, East End. The expression for <math>\sigma</math> should be <math>\sigma^2</math> which may well be my mistake. | **Yuichi** - This seems to be a wonderful start and example of pretty complete note on the materials we discussed today. There may be a few things someone can add, but if the notes for the rest of the semester continue this trend, I feel we will have great lecture notes for this class. Thank you, East End. The expression for <math>\sigma</math> should be <math>\sigma^2</math> which may well be my mistake. [//East End - Fixed. Thanks.//] |
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| | **To go to the next lecture note, click [[lec_notes_0911]]** |
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