Web Reference: To describe dynamical processes, such as radiation decays, scattering and nuclear reactions, we need to study how quantum mechanical systems evolve in time. The evolution of a closed system is unitary (reversible). The evolution is given by the time-dependent Schr ̈odinger equation. Time doesn't have an Operator in Quantum mechanics, but there is a Time Evolution Operator (or Propagator) that tells how a Quantum State evolves in time. Observables (or operators) associated with mutually commuting operators are called compatible. As mentioned before, the treatment of a physical problem can in many cases be reduced to the search for a maximal set of compatible operators.
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