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I just completed my second year of my physics undergraduate degree. And recently did a course on Quantum Mechanics. I have a few questions regarding the basic theory and postulates, probably, because due to lack of full clarity.

So,

Consider a wave function ψ(x,o), which is well behaved and normalized. Which is the wave-function of a particular system initially.

Now, my question is, there are 2 postulates which determine the time evolution of any wave function.

One is the popular Schrodinger equation, which is described using the operator H(Hamiltonian).

The other postulate is, that upon "measurement", the wave function will collapse to one of the eigenvalues of the respective physical variable.

I do not understand the concept of "measurement" precisely, as I could not find that in my book. Is measurement taken as an instantaneous process? If not, then, is the "wave function collapse" postulate a consequence of the Schrodinger equation?

I think of measurement as an interaction with the system, which develops a time varying Hamiltonian, which makes the system evolve in accordance to Schrodinger equation, resulting in a wave function collapse?

If I am thinking the wrong way, then can we not use Schrodinger equation during the process of measurement?

If the wave function collapse is a consequence of Schrodinger equation, then why do es the wave function collapse seems to be a non-deterministic equation i.e is to say, the wave function cannot be uniquely determined after some time t(which is after measurement), while Schrodinger equation uniquely determines the wave function after a time t?

I need to be clear on this, even though it might be a trivial question. :)

Thank you.