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The functional of uncertainty J͓͔ assigns to each state ͉͘ the product of the variances of the momentum and position operators. Its first and second variations are investigated. Each stationary point is located on one of a countable set of three-dimensional manifolds in Hilbert space. For a harmonic oscillator with given mass and frequency the extremals are identified as displaced squeezed energy eigenstates. The neighborhood of the stationary states is found to have the structure of a saddle,doi:10.1103/physreva.53.2084 pmid:9913112 fatcat:c2eamkc7s5fz5oxgyheouuffra