Hello =) I have a question regarding the conservation of probability in quantum mechanics.(adsbygoogle = window.adsbygoogle || []).push({});

We know that the probability of a measurement of a given observable, is preserved in time if the observable commutes with the Hamiltonian.

But this is also true if the value of the measurement rapresented by the eigenvalues is degenerate?

For example, if I have the observable ## \Omega ## which commutes with the Hamiltonian, and suppose that the system state is a linear combination of eigenstates of H and hence of ## \Omega ##, and I want to know the probability that a measurement give me a value of ## \omega_1 ## at any time

##P (\omega_1, t) = | <\omega_1 | Psi, t> | ^ 2 = | <\omega_1 | e ^ {- i / h H} | \Psi, 0> | ^ 2 = | e ^ {- i / h E_1} c_ {1, t = 0} |^ 2 = ##

##= e^ {i / h E_1} \tilde{c} _ {1, t = 0} e^ {- i / h E_1} c_ {1, t = 0} = \tilde {c} _ {1, t = 0 c_ {1}, t = 0} = P (\omega_1, t = 0) ##

but in the degenerate case that is the same thing?

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# [QM] Conservation probability to degenerate eigenvalues

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