(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If A and B were observables, and say the simultaneous eigenkets of A and B [tex]{|a',b'>}[/tex] form a complete orthonormal set of base ket. Can we conclude that [tex][A,B]=0[/tex]?

2. The attempt at a solution

Assume [tex]{|a',b'>}[/tex] is incompatible:

[tex]AB|a',b'>=a'b'|a',b'>[/tex] <-- skipped several steps

[tex]BA|a',b'>=a'b'|a',b'>[/tex]

[tex]AB|a',b'>-BA|a',b'>=0[/tex]

[tex][AB-BA]|a',b'>=0[/tex]

[tex][A,B]|a',b'>=0[/tex]

[tex][A,B]=0[/tex]

and so we reach a contradiction. Therefore, we conclude that [tex][A,B]=0[/tex] assuming the simultaneous eigenkets of A and B [tex]{|a',b'>}[/tex] form a complete orthonormal set of base ket.

was this thought process correct?

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# Homework Help: QM - observables

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