Two questions regarding the quantum mechanical wavefunction I'm just starting with quantum mechanics and I've got some questions.

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*Long after measurement of a position of a particle, does the wavefunction return to the same form, or does an entirely different form emerge that has nothing to do with the first form of the wavefunction of the particle? I mean the expression of the wavefunction.


*Does the "state of the particle" mean the wavefunction at an instant in time, or does it mean the wavefunction including the time dependence of it?
 A: *

*In general, no. The wavefunction undergoes time evolution after the collapse, which may take it to an entirely different form. You can calculate this from the energy eigenstate expansion of the new wavefunction, if you wish.

*Depends on context - if you're talking about a stationary state, then the time dependence is not important. However, if you're talking about a more general state, then time dependence is important, and is generally included with the state $|\Psi\rangle$.

A: In standard QM there are two postulates that givern its evolution:

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*the abstract Schrodinger equation


*the collapse postulate
The first postulate tells us how the quantum wave evolves in the absence of measurements (in Rovelli's relational QM, in the absence of external interactions). It is usually said to be deterministic but this is a strange use of the term when the quantum wave is already indeterministic.
The second postulate tells us how the quantum wave evolves in the presence of a measurement. It evolves indeterministically - that is randomly - and collapses to a quantum eigenwave of the measurement. The associated eigen-value is the value measured by the measurement.
Afterwards, this wave again evolves by the first postulate. All in all, quantum evolution is a kind of punctured evolution: continuous evolution that is punctured every so often to an eigen wave.
