The common wavefunction and annihilation of 1 photon QM says that if we have many particles they have a common wavefunction. Also QM says that when you measure a particle or observe it, you collapse its wavefunction. That must be a logical mistake. Now lets look at a laser beam as an example. The laser produces a plane wave which is comprised by many photons. Now if we observe (annihilate) one photon a part of the wavefunction must collapse. But then this means  that the wavefunction must be comprised by many individual wavefunctions of any separate photon. So it can not be common but a sum of individual wavefunctions (by the way sphearical in form which overlap to build a plane wave). What is your opinion about this issue?
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QM says that if we have many particles they have a common wavefunction.

It is not compulsory. Many particles may have incoherent wavefunctions and be described by a classical density matrix,

Also QM says that when you measure a particle or observe it, you collapse its wavefunction.

Collapse is an anthropomorphic way of talking about mathematics.The wavefunction $Ψ$ of a particle  is a solution of a quantum mechanical equation with given boundary conditions, a complex function. The $Ψ^*Ψ$  is the predicted probability distribution. An interaction, measurement is an interaction too, will pick up one instance of a probability distribution that has to be accumulated to validate the prediction. Many instances are necessary to build up a probability distribution, as in this double slit single electron experiment.

That must be a logical mistake. Now lets look at a laser beam as an example. The laser produces a plane wave which is comprised by many photons.

The laser is a good example of a collective coherent wavefunction which is defined by the whole system, including the lasing source. This MIT video gives a good explanation of the superposition of two coherent laser beams. Superposition is not interaction. It is the addition of the two  beams collective wavefunctions.

Now if we observe (annihilate) one photon a part of the wavefunction must collapse.

We cannot observe one photon out of the zillions in the laser $Ψ$ .
One can make the laser beam very weak so that individual photons can be recorded, and their wave function retains the coherence to show the probability distribution as seen in this double slit experiment single photon at a time. The collective wave function and its complex conjugate squared are there, even for one photon.

But then this means that the wavefunction must be comprised by many individual wavefunctions of any separate photon. So it can not be common but a sum of individual wavefunctions (by the way sphearical in form which overlap to build a plane wave).

Note, it is wavefunctions and they have phases and can be coherent building the mathematics of one collective coherent wavefunction , two or many they are complex functions.  BUT the probability is the total $Ψ^*Ψ$, a real distribution .

What is your opinion about this issue?

Once the boundary conditions are set , the measurement picks up a probability instant.
