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Feb 3, 2017 at 10:43 comment added Daniel In case anyone else runs into this problem, there are more mistakes above, although I haven't carefully checked it. Probably $T\dot a T^{-1}=-\dot a$ as well.
Jan 17, 2017 at 17:09 comment added udrv You have $a = \sqrt{\omega/2\hbar}\left(q +(i/\omega) p \right) $ and $TaT^{-1} = \sqrt{\omega/2\hbar}\left( TqT^{-1} - (i/\omega) TpT^{-1} \right] = \sqrt{\omega/2\hbar}\left(q - (i/\omega) (-p) \right] = a$, not $TaT^{-1} = a^\dagger$. Similarly for $a^\dagger$.
Jan 16, 2017 at 16:52 history asked Daniel CC BY-SA 3.0