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In this work, we apply a meshless method to some problems drawn from the context of quantum mechanics. We investigate eigenvalue problems -the time-independent Schrödinger's equation -and boundary value problems as well, these last illustrated by the Nonlinear Schrödinger equation. Meshless methods require absolutely no meshes, unlike the Finite Element Method (FEM), which turns out to be a great advantage when dealing with three-dimensional problems. In a particular class of meshless methods,doi:10.1108/03321641111168084 fatcat:yngrbqf3brb5tdiiwyuwtcw4ge