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Nambu Quantum Mechanics, proposed in Phys. Lett. B536, 305 (2002), is adeformation of canonical Quantum Mechanics in which the manifold over which the"phase" of an energy eigenstate time evolves is modified. This generalizationaffects oscillation and interference phenomena through the introduction of twodeformation parameters that quantify the extent of deviation from canonicalQuantum Mechanics. In this paper, we constrain these parameters utilizingatmospheric neutrino oscillation data, and $B^0$-$\overline{B^0}$ oscillationdata from Belle. Surprisingly, the bound from atmospheric neutrinos is strongerthan the bound from Belle. Various features of Nambu Quantum Mechanics are alsodiscussed.

Constraints on a Generalization of Geometric Quantum Mechanics from Neutrino and $B^0$-$\overline{B^0}$ Oscillations