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Der Hamiltonoperator des Harmonischen Oszillators in der Quantenmechik lautet\
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dazugeh\[ODoubleDot]rigen Wellenfunktionen auszurechnen basiert auf der sog. \
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Cell["Auf - und Absteigeoperatoren", "Subsubsection",
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a = ( x+ i p)/Sqrt[2]
ac = (x - i p)/Sqrt[2]
(Beachte: \"a\" und \"ac\" sind Operatoren!)\
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Aus der Kommutatorrelation [x, p] = i folgt unmittelbar
[a, ac] = 1 \
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Au\[SZ]erdem kann der Hamiltonoperator folgenderma\[SZ]en geschrieben werden : 
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Es kann gezeigt werden, dass gilt:
a  |n> =  Sqrt[n]       |n-1>
ac|n> =  Sqrt[n+1]  |n+1>
( |n> sind die Eigenzust\[ADoubleDot]nde von H: H|n> = En |n> )
Damit ergeben sich folgende Energieeigenwerte:  
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a[f] und ac[f]  k\[ODoubleDot]nnen nun verwendet werden, um
1. die Grundzustandswellenfunktion zu berechnen,
2. alle angeregten Wellenfunktionen zu berechen,
3. Orthogonalit\[ADoubleDot]t und Normierung zu \[UDoubleDot]berpr\
\[UDoubleDot]fen,
4. Zeitliche Entwicklung von Zust\[ADoubleDot]nden zu betrachten.\
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zu 3. Orthogonalit\[ADoubleDot]t und Normierung \
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