A general theme is Quantum Mechanics is "What is the asymptotics of the so-called quantum observables?". An analogue of this question in Riemannian geometry is "What is the asymptotics of the eigenfunctions of the Laplacian?". A recent result of Burns, Guillemin and Uribe gives a method to approach the first question on toric varieties endowed with a special metric, the so called reduced metric . In this talk we will explain their result and how it generalizes to all toric metrics. We will also speak about an unexpected connection between this result and an important problem in Kähler geometry namely that of approximating Kähler metrics by algebraic ones.