On Essential Self-Adjointness for Magnetic Schrödinger and Pauli Operators on the Unit Disc in

We study the question of magnetic confinement of quantum particles on the unit disk in , i.e. we wish to achieve confinement solely by means of the growth of the magnetic field near the boundary of the disk. In the spinless case, we show that , for close to 1, insures the confinement provided we assume that the non-radially symmetric part of the magnetic field is not very singular near the boundary. Both constants and are optimal. This answers, in this context, an open question from Colin de Verdière and Truc (Ann Inst Fourier 2011 , Preprint, arXiv:0903.0803v3). We also derive growth conditions for radially symmetric magnetic fields which lead to confinement of spin 1/2 particles.