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Slide46 - Hennitian Operators The eigenvalues ofHerInitian...

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Unformatted text preview: Hennitian Operators The eigenvalues ofHerInitian operators must be real. Proof: Jig/2mg! and Iw(&w)*dr:J-yl*jl,cdr Iw(aw)*d'r: IW*0WT Iqa“ w*d'r : Iw*aupdr a*Iw*vdr = aIder (a*—a)Iw*Wr =0 (a*—a)flw‘2dr : 0 Since 927 = 0 is not a valid wavefinietiona = (1* = real number In a similar manner, it can be proven that for a Hermitian operator the expectation value <a> = {a}* = real quantity. ...
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