Two hermitian commutator anticommut {A,B}=AB+BA=0

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The discussion centers on the properties of two Hermitian operators, A and B, that anticommute, defined by the relation {A,B} = AB + BA = 0. It raises the question of whether a simultaneous eigenket of A and B can exist. The conclusion suggests that assuming |v> is an eigenvector of both A and B allows for the application of the anticommutator, leading to further insights into the implications of this relationship.

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dustu
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Two hermitian commutator anticommute: {A,B}=AB+BA=0.Is it possible to have a simultaneous eigenket of A and B?illustrate...
Thank you in advance
 
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Sounds like homework?

Cheers,

Jazz

EDIT: Anyway, just assume that |v> is an eigenvector to A and B, then apply the anticommutator to it and draw your conclusions.
 
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