We investigate the existence of Mumford’s Approximately Macroscopically Unique (AMU) states in quantum systems generated by unbounded self-adjoint operators with small commutators. In particular, we show that AMU states always exist for the standard position–momentum systems when the Planck constant $|\hbar|$ is sufficiently small. On the other hand, we demonstrate that these classical quantum mechanical systems remain fundamentally distant from classical mechanical systems, even in the limit $|\hbar| \to 0$. This is joint work with Huaxin Lin.