I and my friend were disputing about some weird behaviour of the act of measuring some observables quantities e.g. Energy, position.
But I still don't think what he said is strictly true.
He said" each observable has its own Eigenstate, and when you measure it, the wave function will collapse to that eigenstate , giving its eigenvalue for that particle observable quantity. However ,I think some observables do share same eigenstate. i.e. a free particle with zero potential, you can prove this by Solving the TISE. When you now measure and obtained an exact momentum of a particle of a system, by uncertainty principle, the uncertainty of $x$ will be infinite, then the wave function will be spread everywhere,therefore it has a well define wavelength, thus you have well defined $k$ for wavenumber, hence a well defined energy by $p^2 / 2m$.
To conclude, He said: is it true that every time you measure a quantity, it only produces a eigenstate for that particular quantity? I.e. measure position gives position eigenstate, momentum for momentum eigenstate.
My argument shown above claimed the above is not strictly true: So my argument is energy and momentum do share same eigenfunction, when potential is zero. Who is correct?
I also mentioned something called "Conjugate variables" e.g. position and momentum, you can only know one at a time. But I think energy and momentum are not, hence resulting in the reasoning i wrote above!