# Re-entering superposition

I've realized that I'm somewhat familiar with what happens when an system in a superposition is "measured". But not at all with what happens after.

Example: If there is an electron in a superposition, it is measured and collapses to an eigen basis, what happens after? Does it instantly become a coherent system again? Or does it spend some time in this "collapsed" state?

The example is for an electron, but I'm interested in quantum systems in general.

Assume that your spin has been prepared aligned along x axis (eigenstate of $\sigma_x$). Your spin is in a superposition of state having $\sigma_z$ eigenvalue +1 and -1. When you actually measure the spin along z it will collapse on one of the eigenstate.It will then remain in this state (as long as you do not measure it along another direction), in particular you can perform multiple time the measurement of the spin along z and you will get again and again the same result ($\pm1$) that you get on the first measure.
• So, what you're basically telling me, is that after a measurement, if we do not measure again, the spin along $z$ will never enter a superposition? – Anton Jan 21 '16 at 15:38
• It will depend of the Hamiltonian (time evolution) but in absence of interaction the eigenvector of $\sigma_z$ are also eigenvector of $H$... – floqui Jan 21 '16 at 15:41