Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields
Ricardo Cordero-Soto, Raquel Lopez, Erwin Suazo and Sergey K. Suslov http://arXiv.org/abs/0801.3246
Abstract: We consider an old Landau problem -- the motion of a charged particle with a spin in uniform magnetic and perpendicular electric fields that are changing with time in our case. The corresponding Green function (or Feynman's propagator) is found as an elementary function of certain integrals of a characteristic function and the electromagnetic fields; see equation (6.14) from the attached paper. You may appreciate appearance of Bessel functions of order 1/4 in the case of linear magnetic field; see equations (7.5)-(7.6).