Simple shell model for quantum dots in a tilted magnetic field

A model for quantum dots is proposed, in which the motion of a few electrons in a three-dimensional harmonic oscillator potential under the influence of a homogeneous magnetic field of arbitrary direction is studied. The spectrum and the wave functions are obtained by solving the classical problem. The ground state of the Fermi system is obtained by minimizing the total energy with regard to the confining frequencies. From this a dependence of the equilibrium shape of the quantum dot on the electron number, the magnetic field parameters, and the slab thickness is found.