- #1
good_phy
- 45
- 0
Hi.
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?
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?