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I'm getting a bit confused on the dimensionality of the wavefunction. I've seen the wavefunction described as:

(1) A vector of norm 1 in a finite dimensional Hilbert Space

(2) A vector of norm 1 in an infinite dimensional Hilbert Space

(3) A continuos function (it is my understanding that there can be equivalences between infinite dimensional spaces and functions ie. fourier series etc., is this what is happening here?)

Also, I'd like to make some statements and verify that they are correct:

* Observables are self-adjoint operators that act on the wavefunction

* The effect of a measurement is to force the state of the system to an eigenvector of the operator and the result of the measurement is the associated eigenvalue of that eigenvector

* Do self-adjoint operators always have n distinct eigenvalues? (where n is the dimensionality of the Hilbert space?)

Thanks!

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# Wavefunction Dimensionality

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