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PDF-SincetheoperatorsAandBcontainXandP,[A;B]givesusthecommutatorofXandP,wh PDF document

2mm2X2 2 mX2 2P2 2m8 r m 2XiP p 2m r m 2XiP p 2mi 2XPPX9aya1 2iiN1 2whereweveusedaknowncommutatorandthede nitionsofayaandNthecreationannihilatio

2m+m!2X2 2!=~! m!X2 2~+P2 2m~!!=~!8: r m! 2~XiP p 2m~!! r m! 2~X+iP p 2m~!!i 2~(XPPX)9=;=~!aya+1 2i~(i~)=~!N+1 2wherewe'veusedaknowncommutatorandthede nitionsofay andN(thecreation annihilatio

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SincetheoperatorsAandBcontainXandP,[A;B]givesusthecommutatorofXandP,wh: Transcript

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