In the mathematical formulation of quantum mechanics, any pair of non-commuting self-adjoint operators representing observables are subject to similar uncertainty limits.

In the mathematical formulation of quantum mechanics, states are given by non-zero vectors in a Hilbert space V ( where two vectors are considered to specify the same state if, and only if, they are scalar multiples of each other ) and observables are given by self-adjoint operators on V. However, as indicated below, not every self-adjoint operator corresponds to a physically meaningful observable.

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