  In this article we consider a 2-D quantum particle confined a disc whose
radius can be deformed continuously in time. We study the problem of
controllability of such a quantum particle via deformations of the initial
disc, i.e., when we set the time-dependent radius of the disc to be control
variable. We prove that the resulting system is locally controllable around
some radial trajectories which are linear combinations of the first three
radial eigenfunc-tions of the Laplacian in the unit disc with Dirichlet
boundary conditions. We prove this result, thanks to the linearisation
principle, by studying the linearised system, which leads to a moment problem
that can be solved using some results from Nonharmonic Fourier series. In
particular, we have to deal with fine properties of Bessel functions.
