Geometrical phase for a three-dimensional anisotropic quantum well
  A three-dimensional anisotropic quantum well placed in an adiabatically precessing uniform magnetic field is considered and an explicit formula for the Berry phase is obtained. To get the Berry phase, a purely algebraic algorithm of reducing a quadratic Hamiltonian to the canonical form via symplectic transformations of the phase space is presented. 
V. A. Geyler, A. V. Shorokhov