Question: Show that two noncommuting operators cannot have a complete set of common eigenfunctions. Show that if P and Q have a complete set of common

Show that two noncommuting operators cannot have a complete set of common eigenfunctions. Show that if P̂ and Q̂ have a complete set of common eigenfunctions, then [P̂,Q̂] f = 0 for any function in Hilbert space.

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