Projection operators operate on wavefunction and project onto space or time coordinate, or energy or momentum vector, to give discrete positive real values (eigenvalue) {direct measurement}, which are all possible outcomes, each with probability. Experimenters can know possible measured values and predict probabilities. However, values may be less than quantum sizes and so not measurable. Operators have same dimensions as particle.
Alternatively, experimenters can prepare a quantum system in a known initial state, have particle interact with prepared quantum system, separate particle and prepared quantum system, and then measure quantum-system state {indirect measurement}. Indirect measurements require entangling particle and prepared quantum system, to couple their states. Wavefunction collapse puts quantum system into a state that indirectly determines particle state. Quantum system can have same or more dimensions as particle.
Physical Sciences>Physics>Quantum Mechanics>Wavefunction>Collapse>Measurement>Operators
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Date Modified: 2022.0224