1 2

これを IMAGE imgs/uncert.dvi38.gif

IMAGE imgs/uncert.dvi39.gif

IMAGE imgs/uncert.dvi40.gif


IMAGE imgs/uncert.dvi41.gif


IMAGE imgs/uncert.dvi42.gif


IMAGE imgs/uncert.dvi43.gif


IMAGE imgs/uncert.dvi44.gif


IMAGE imgs/uncert.dvi45.gif


IMAGE imgs/uncert.dvi46.gif


IMAGE imgs/uncert.dvi47.gif


IMAGE imgs/uncert.dvi48.gif


IMAGE imgs/uncert.dvi49.gif


IMAGE imgs/uncert.dvi50.gif


IMAGE imgs/uncert.dvi51.gif


IMAGE imgs/uncert.dvi52.gif


IMAGE imgs/uncert.dvi53.gif


演算子 IMAGE imgs/uncert.dvi55.gif

固有値

のそれぞれ

IMAGE imgs/uncert.dvi56.gif

IMAGE imgs/uncert.dvi54.gif

を固有値とする固有関数

IMAGE imgs/uncert.dvi57.gif

IMAGE imgs/uncert.dvi58.gif

式

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に右から

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すなわち

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は

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かつ

IMAGE imgs/uncert.dvi64.gif

IMAGE imgs/uncert.dvi65.gif

このように IMAGE imgs/uncert.dvi66.gif

は IMAGE imgs/uncert.dvi67.gif

の固有関数を

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の表現

IMAGE imgs/uncert.dvi69.gif

IMAGE imgs/uncert.dvi70.gif

式 IMAGE imgs/uncert.dvi71.gif を

IMAGE imgs/uncert.dvi73.gif

IMAGE imgs/uncert.dvi72.gif

IMAGE imgs/uncert.dvi74.gif

IMAGE imgs/uncert.dvi75.gif

IMAGE imgs/uncert.dvi76.gif

ここで式

IMAGE imgs/uncert.dvi77.gif

から式 IMAGE imgs/uncert.dvi78.gif

両辺に左から


IMAGE imgs/uncert.dvi80.gif

IMAGE imgs/uncert.dvi79.gif

IMAGE imgs/uncert.dvi81.gif

これを IMAGE imgs/uncert.dvi82.gif

IMAGE imgs/uncert.dvi83.gif