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Poisson- Klammern
2011-07-02T13:20:37Z
<p>82.198.28.221: /* Bezug zur Quantenmechanik */</p>
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<div><noinclude>{{Scripthinweis|Mechanik|4|6}}</noinclude><br />
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Jede Observable läßt sich in der klassischen Mechanik als Funktion von Ort, Impuls und Zeit darstellen:<br />
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:<math>Observable=g(\bar{q},\bar{p},t)</math><br />
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Die zeitliche Änderung längs der Bahn <br />
:<math>\bar{q}(t),\bar{p}(t)</math><br />
im Phasenraum <br />
:<math>\Gamma </math><br />
:<br />
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:<math>\frac{dg(\bar{q},\bar{p},t)}{dt}=\sum\limits_{i=1}^{f}{\left( \frac{\partial g}{\partial {{q}_{i}}}{{{\dot{q}}}_{i}}+\frac{\partial g}{\partial {{p}_{i}}}{{{\dot{p}}}_{i}} \right)}+\frac{\partial g}{\partial t}=\sum\limits_{i=1}^{f}{\left( \frac{\partial g}{\partial {{q}_{i}}}\frac{\partial H}{\partial {{p}_{i}}}-\frac{\partial g}{\partial {{p}_{i}}}\frac{\partial H}{\partial {{q}_{i}}} \right)}+\frac{\partial g}{\partial t}=:\left\{ g,H \right\}+\frac{\partial g}{\partial t}</math><br />
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====Definition:====<br />
Für zwei beliebige Observablen <br />
:<math>g(\bar{q},\bar{p},t)</math> und <math>f(\bar{q},\bar{p},t)</math><br />
heißt<br />
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:<math>\sum\limits_{i=1}^{f}{\left( \frac{\partial g}{\partial {{q}_{i}}}\frac{\partial f}{\partial {{p}_{i}}}-\frac{\partial g}{\partial {{p}_{i}}}\frac{\partial f}{\partial {{q}_{i}}} \right)}=:\left\{ g,f \right\}</math><br />
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Poisson- Klammer<br />
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Well put, sir, well put. I'll certinlay make note of that.<br />
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