I Measuring Spin in the Stern Gerlach Experiment

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1. Nov 19, 2016

klen

When we are measuring the spin of the electron in the experiment, we choose the spin property as its eigen state for the measurement. The eigen vectors corresponding to these states could be time dependent. Can we still break the problem into solving time independent Schrodinger Equation and then multiplying by a time dependent function, like we do for the case of measurement of energy? How do we calculate the spin eigen vectors using Schrodinger Equation?

2. Nov 19, 2016

Simon Bridge

In the representation you are talking about, it is the state vector that is time dependent... not the eigenstates.
$\psi = c_1(t)\psi_1+c_2(t)\psi_2: c_1^\star c_1+c_2^\star c_2 = 1$ ... so $\psi_1$ and $\psi_2$, the eigenstates, are solutions to the time independent schrodinger equation.
... so what was your question there?

3. Nov 20, 2016

klen

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?

Last edited: Nov 20, 2016
4. Nov 20, 2016

Staff: Mentor

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.