Like all beginners to QM I'm really confused about the measurement operation. I understand that measurement is simply a dot product with an "operator" and the result is one of the operator's eigenvalues. Now my question is what exactly is an operator? If someone could explain what physical entity is an operator in the following situations that would help me understand this better. 1. A particle moving at some velocity hits a wall/detector. Till it hits the detector its position is described by a combination of position eigenstates. Once it hits the detector its position becomes a single eigenvalue. Is the wall an operator here? 2. A particle moves through an SG apparatus. Till it passes through the apparatus its spin state is a combination of two eigenstates (in some axis). Once it moves through the magnetic field its spin state becomes one of the eigenstates. Is the magnetic field an operator here?