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Simon Bridge

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##\psi = c_1(t)\psi_1+c_2(t)\psi_2: c_1^\star c_1+c_2^\star c_2 = 1## ... so ##\psi_1## and ##\psi_2##, the eigenstates, are solutions to the time independent schrodinger equation.

... so what was your question there?

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I believe only the eigen states of energy are the stationary states and do not depend on time, so if we are measuring spin eigen states, they could be time dependent. Isn't the time independent Schrodinger equation a energy eigen value equation?

##\psi = c_1(t)\psi_1+c_2(t)\psi_2: c_1^\star c_1+c_2^\star c_2 = 1## ... so ##\psi_1## and ##\psi_2##, the eigenstates, are solutions to the time independent schrodinger equation.

... so what was your question there?

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It is. However, if two operators commute they will have shared eigenstates, and ##S_z## commutes with the Hamiltonian. Thus there are states that are eigenstates of both energy and spin, and both remain constant over time.I believe only the eigen states of energy are the stationary states and do not depend on time, so if we are measuring spin eigenstates, they could be time dependent. Isn't the time independent Schrodinger equation a energy eigenvalue equation?

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