Spontaneous Symmetry Breakdown in non-relativistic Quantum Mechanics
  The advantages and disadvantages of some pedagogical non-relativistic quantum-mechanical models, used to illustrate spontaneous symmetry breakdown, are discussed. A simple quantum-mechanical toy model (a spinor on the line, subject to a magnetostatic interaction) is presented, that exhibits the spontaneous breakdown of an internal symmetry. 
R. Munoz-Vega, A. Garcia-Quiroz, Ernesto Lopez-Chavez, Encarnacion   Salinas-Hernandez
math-ph hep-th math.MP