Compendium of Quantum Physics

pp 284-287

Hidden Variables

  • Basil J. Hiley

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Standard quantum mechanics, in the hands of von Neumann, makes the assumption that the ► wave function, ψ(r, t), provides the most complete description of state of an evolving system. It then uses the Born probability postulate (► Born rule) and assumes that the probability of finding the system at position r at time t is given by P = |ψ(r, t)|2. This gives an essentially statistical theory, ► probability interpretation but a statistical theory unlike those found in classical situations where all the dynamical variables such as position, momentum, angular momentum etc., are well defined but unknown.

The dynamical variables of a quantum system are determined by the eigenvalues of operators called ► ‘observables’. Given a quantum state, not all the dynamical variables have simultaneous values. For example, if the position is sharply defined, then the momentum is undefined and vice-versa. In other words there exist sets of complementary variables such that if one set are well defined, the other set are completely undefined. This is the feature that underlies the ► Heisenberg uncertainty principle.