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Do you know eigenfunction of inverse operator, for instance [itex] \hat{A^{-1}} [/itex] given that [itex] \hat{A}\varphi = a\varphi[/itex]

textbook said eigenfunction of inverse operator A is the same as [itex] \varphi [/itex]

which eigenvalue is [itex] \frac{1}{a} [/itex]

Can you prove that?

And is it really that [itex] [A,A^{-1}] = 0 [/itex] so both opreatator have a common

eigenfunction if eigenvalue is not degenerate, this theorem is called commutator theorem?

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# [Q]Eigenfunction of inverse opreator and another question.

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