nLab classical-to-quantum notions - table

	classical mechanics	semiclassical approximation	…	formal deformation quantization	quantum mechanics
order of Planck's constant $\hbar$	$\mathcal{O}(\hbar^0)$	$\mathcal{O}(\hbar^1)$	$\mathcal{O}(\hbar^n)$	$\mathcal{O}(\hbar^\infty)$
states	classical state	semiclassical state			quantum state
observables	classical observable				quantum observable