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As I understand it, you can make a measurement on a particle and if you quickly carry out a second measurement you will get the same outcome as the prior measurement. If this is the case, how much time do you have between measurements before the wave function begins to evolve according to Schrodinger's equation and then any subsequent measurement will be different from the prior measurement?

Thanks

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The evolution immediately after the measurement occurs according to the Schrödinger equation, but now with a known initial state. In general, in order to be able to "repeat" a measurement you have to prepare the state again.

For example, say I have a particle in a harmonic oscillator potential prepared in the state

$$|\psi\rangle = \frac{1}{\sqrt{2}}|0\rangle + \frac{1}{\sqrt{2}}|1\rangle $$

I measure its energy and find it to be $\frac{\hbar \omega}{2} $, indicating the particle was found in the $|0\rangle$ state.

Because $|0\rangle$ is an energy eigenstate, time evolution will not change it, so any subsequent measurement will continue to give the same value for the energy: $\frac{\hbar \omega}{2}$. In order to perform a "repeat" of the original measurement you have to prepare the state $|\psi\rangle$ again.

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