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We introduce a minimalistic notion of semiclassical quantization and use it to prove that the convex hull of the semiclassical spectrum of a quantum system given by a collection of commuting operators converges to the convex hull of the spectrum of the associated classical system. This gives a quick alternative solution to the isospectrality problem for quantum toric systems. If the operators are uniformly bounded, then the convergence is uniform. Analogous results hold for non‐commuting operators.

Semiclassical quantization and spectral limits of ħ‐pseudodifferential and Berezin–Toeplitz operators