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classes:2009:fall:phys4101.001:lec_notes_0911 [2009/09/14 19:17] – ykclasses:2009:fall:phys4101.001:lec_notes_0911 [2009/09/23 22:43] (current) – yk
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-===== Sept 11 (Fri) ===== +===== Sept 11 (Fri) Probability interpretation ===== 
-** Responsible party: Schrödinger's Dog, Devlin**+** Responsible party: Schrödinger's Dog**
  
-**To go back to the lecture note list, click [[lec_notes]]**+**To go back to the lecture note list, click [[lec_notes]]**\\ 
 +**previous lecture note: [[lec_notes_0909]]**\\ 
 +**next lecture note: [[lec_notes_0914]]**\\
  
 +**[[Q_A]]**
  
 === Main points === === Main points ===
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 Then, <math>\lim_{\Delta t\rightarrow 0} \frac{\int_{-\infty}^{\infty} f(x+\Delta x,t+\Delta t) dx - \int_{-\infty}^{\infty} f(x,t) dx}{\Delta t} = \lim_{\Delta t\rightarrow 0} \frac{\int_{-\infty}^{\infty} \frac{\partial f(x,t)}{\partial t}\Delta t dx + \frac{\partial f(x,t)}{\partial x}\Delta x dx}{\Delta t} = \int_{-\infty}^{\infty} \frac{\partial f(x,t)}{\partial t} dx + \Delta x[f(x,t)]_{-\infty}^{\infty}</math>.  Provided that <math>f(x,t)</math> is a normalizable function, the last term should be zero. Then, <math>\lim_{\Delta t\rightarrow 0} \frac{\int_{-\infty}^{\infty} f(x+\Delta x,t+\Delta t) dx - \int_{-\infty}^{\infty} f(x,t) dx}{\Delta t} = \lim_{\Delta t\rightarrow 0} \frac{\int_{-\infty}^{\infty} \frac{\partial f(x,t)}{\partial t}\Delta t dx + \frac{\partial f(x,t)}{\partial x}\Delta x dx}{\Delta t} = \int_{-\infty}^{\infty} \frac{\partial f(x,t)}{\partial t} dx + \Delta x[f(x,t)]_{-\infty}^{\infty}</math>.  Provided that <math>f(x,t)</math> is a normalizable function, the last term should be zero.
  
 +==Schrodinger's Dog== 
 +Thanks Yuichi, this makes a lot more sense!
 ==End of lecture== ==End of lecture==
      
 S.D.: I wasn't really clear on the last proof, but feel that it isn't a important detail. Besides that, the rest of the lecture was great! S.D.: I wasn't really clear on the last proof, but feel that it isn't a important detail. Besides that, the rest of the lecture was great!
            
 +**To go back to the lecture note list, click [[lec_notes]]**\\
 +**previous lecture note: [[lec_notes_0909]]**\\
 +**next lecture note: [[lec_notes_0914]]**\\
 +
classes/2009/fall/phys4101.001/lec_notes_0911.1252973840.txt.gz · Last modified: 2009/09/14 19:17 by yk

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