# Question Concerning Superposition

I'm wondering if a system regains its superposition after it's observed or if it remains a definite value forever after observation. Also, if a system does regain its superposition, does it occur instantly after it's done being measured?

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You could regard the arrival of a train as a superposition until the train is seen to arrive.
It's having arrived, either you get on to the train if that was the plan, or maybe you meet somebody getting off it.
The train cannot return to the state of having not yet arrived.

jfizzix
Gold Member
The state is always in some superposition..
If it is a single eigenstate of one observable, it may be in a superposition of multiple eigenstates of another observable.

If you measure an observable of a particle, its wavefunction can be said to collapse to a single eigenstate of that observable.

Before and after that, the state evolves according to how its energy depends on its position, momentum, and other observables (i.e., its Hamiltonian).

If a particular observable is a conserved quantity (commutes with the Hamiltonian), and you measure that observable, the state after measurement will always be the same eigenstate of that observable.

If the observable is not conserved (does not commute with the hamiltonian), then after a sufficient time, the state will be in a reasonable superposition of multiple eigenstates of the observable in question.

Another way of looking at it:
The uncertainty principle tells us that a particle cannot at the same time be in a single eigenstate of all ovservables.

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bhobba
Nugatory
Mentor
I'm wondering if a system regains its superposition after it's observed or if it remains a definite value forever after observation. Also, if a system does regain its superposition, does it occur instantly after it's done being measured?
The system doesn't return to its previous state. The measurement puts it in an eigenstate of whatever we're measuring. After the measurement the state evolves forward from there according to Schrodinger's equation.

That evolution may put it into a new superposition or it may leave whatever we measured in a definite value forever (or at least until the next interaction disturbs it); this depends on whether the observable commutes with the Hamiltonian or not.

bhobba