Decoherence time and spin measurement in the Stern-Gerlach experiment

We present an analytical solution to the decoherence time for the spin measurement and the diagonalization of the density matrix of spin variables in the Stern-Gerlach experiment. This solution requires the calculation of the Pauli spinor with a spatial extension, which is not found in quantum mechanics textbooks. With this full spinor and the measured position of the particle we demonstrate the three postulates of quantum measurement: quantization, spectral decomposition and wave function reduction. The transition from a quantum superposition to a statistical mixture is well explained in this way, but not the single result that always emerges from a particular experiment. The spinor spatial extension also allows the introduction of the de Broglie-Bohm trajectories which give a very simple explanation of the particles' impact