Quantum mechanics thread (pop-sci free zone)

No.11269055 ViewReplyOriginalReport
I'll start with a couple of questions.

1. We say that I_z(psy_lambda_mu) = mu*psi_lambda_mu
then we introduce ladder operators and for the plus operator obtain pic related

Why is there a constant in yellow line? Doesn't it follow that I_+ is just psi_lambda_(mu + 1) if you just compare spectral equations for I_z on psi_lambda_(mu + 1) and I_z on [I_+(psi_lambda_mu)]?

2. https://youtu.be/tiXP6dND6SY?list=PL6i60qoDQhQGaGbbg-4aSwXJvxOqO6o5e&t=1016

How do we know that an operator that would change psi(t) to psi(t + T) exists?
Is this operator being self-adjunct (U^+ = U^-1) just an educated guess we make SO THAT the orthogonality of states of the system doesn't change?


Feel free to ask yours/discuss shit, as long as it's not pop-sci level - I think we have enough of that in SQTDDT and just a lot of threads.