I was always curious how scientists achieve a particle with particular wavefunction (of location and spins etc.)
So how do they achieve it? Or is this impossible?
I guess that the procedure of preparation achieves this. Start with a bunch of particles of the desired type. Build a measurement device which measures an observable which has as eigenstate the wavefunction you want to achieve. Observe the particles, each of them will end up in one of the eigenstates of the observable. Select only those which you want. For example, to prepare an electron in a particular spin state, say +1/2 along the z axis, start with some electrons and a Stern-Gerlach device. Orient the Stern-Gerlach device along the z axis. Pass the electrons through it. Keep only the electrons with spin +1/2 (they will be separated from those of spin -1/2).
Please note that the particular wavefunction is obtained up to a phase factor.
Peres saids in his book "Quantum Theory: Concepts and Methods" that for each state of a particle there is a test, i.e. an observable, which has as eigenstate that particular state. If this is achievable in practice, then one should be able to prepare the particle in any state we wish (up to a phase). Probably in practice there are also more sophisticated methods, but I can't tell you more.