Week of 1/14/08
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| + | {{PDF|filename=1_14_08.pdf|title=Lecture notes for 1/14/08: more probability, Gaussians}} | ||
| + | {{PDF|filename=Supplement1_14_08.pdf|title=Supplement for 1/14/08: an arm-waving "derivation" of Schrodinger's equation}} | ||
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| + | ===Some simple Mathematica examples=== | ||
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| + | x = Table[Random[], {i, 100}] | ||
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| + | ListPlot[x] | ||
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| + | Mean[x] | ||
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| + | Variance[x] | ||
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| + | y = Table[Random[Integer],{i,100}] | ||
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| + | z = Table[Random[Real, {10, 11}], {i, 100}] | ||
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{{Mathematica|filename=Centrallimit.nb|title=How coin tossing leads to a Gaussian}} | {{Mathematica|filename=Centrallimit.nb|title=How coin tossing leads to a Gaussian}} | ||
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{{Mathematica|filename=BasicGaussians.nb|title=Basic Properties of Gaussians}} | {{Mathematica|filename=BasicGaussians.nb|title=Basic Properties of Gaussians}} | ||
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| − | [http://www.shodor.org/interactivate/activities/ some useful java applets illustrating probability] | + | |
| + | [http://www.shodor.org/interactivate/activities/ some useful java applets illustrating probability. Click on probablity.] | ||
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| + | ===1/16/08=== | ||
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| + | [http://www.kfunigraz.ac.at/imawww/thaller/visualization/vis.html some very nice QM visualizations] | ||
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| + | {{PDF|filename=1-16-08.pdf|title=Lecture notes for 1/16/08: probability amplitudes, conservation of probability, ensembles, momentum as an operator}} | ||
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| + | ===1/18/08=== | ||
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| + | [http://ticc.mines.edu/csm/wiki/images/2/29/Orthogonal_projection.pdf Refresher from Fall07 PH311 class on functions as elements of vector spaces. 2/22/07.] | ||
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| + | {{PDF|filename=1_18_08.pdf|title=Lecture notes from 1/18/08: vectors in infinite dim. spaces, operators, Q(x,p) -> Q(x, -ihd/dt)}} | ||
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| + | You'll get a chance to prove Ehrenfest's theorem in problem 1.7. | ||
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| + | [[Image:Ehrenfest.jpg]] | ||
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| + | Image from the St. Andrews history page linked here: | ||
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| + | [http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Ehrenfest.html Paul Ehrenfest biography] | ||
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| + | '''If you've forgotten your Fourier Series, please review this before we start Chapter 2.''' | ||
Latest revision as of 16:01, 21 January 2008
 Download Lecture notes for 1/14/08: more probability, Gaussians
|
| Download Supplement for 1/14/08: an arm-waving "derivation" of Schrodinger's equation
|
Some simple Mathematica examples
x = Table[Random[], {i, 100}]
ListPlot[x]
Mean[x]
Variance[x]
y = Table[Random[Integer],{i,100}]
z = Table[Random[Real, {10, 11}], {i, 100}]
 Download How coin tossing leads to a Gaussian
|
| Download Basic Properties of Gaussians
|
some useful java applets illustrating probability. Click on probablity.
1/16/08
some very nice QM visualizations
| Download Lecture notes for 1/16/08: probability amplitudes, conservation of probability, ensembles, momentum as an operator
|
1/18/08
Refresher from Fall07 PH311 class on functions as elements of vector spaces. 2/22/07.
| Download Lecture notes from 1/18/08: vectors in infinite dim. spaces, operators, Q(x,p) -> Q(x, -ihd/dt)
|
You'll get a chance to prove Ehrenfest's theorem in problem 1.7.
Image from the St. Andrews history page linked here:
If you've forgotten your Fourier Series, please review this before we start Chapter 2.
