Decoherence time and spin measurement in the Stern-Gerlach experiment

Michel Gondran (1) , Alexandre Gondran (2) , Abdel Kenoufi (3)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 ENAC - Ecole Nationale de l'Aviation Civile
3 SCORE

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.

Mots clés: Stern & Gerlach; decoherence; postulates of quantum measurement; Pauli spinor; density matrix

Domaines: Optimisation et contrôle [math.OC]

Michel Gondran, Alexandre Gondran, Abdel Kenoufi. Decoherence time and spin measurement in the Stern-Gerlach experiment. AIP 2011, American Institue of Physics Conference on General Problems of Quantum Mechanics, Jun 2011, Växjö, Sweden. pp 116-120, ⟨10.1063/1.3688960⟩. ⟨hal-00938521⟩