Quantum mechanical formalism of particle beam optics

A general procedure for construction of the formalism of quantum beam optics for any particle is reviewed. The quantum formalism of spin-1/2 particle beam optics is presented starting {\em ab initio} with the Dirac equation. As an example of application the case of normal magnetic quadrupole lens is discussed. In the classical limit the quantum formalism leads to the well-known Lie algebraic formalism of classical particle beam optics.Comment: ReVTeX 06 pages, in Proc. of the 18th Advanced ICFA Beam Dynamics Workshop on Quantum Aspects of Beam Physics (QABP) (15-20 October 2000, Capri, ITALY) Editor: Pisin Chen (World Scientific, Singapore, 2002) http://www.pd.infn.it/~khan/ and http://www.imsc.ernet.in/~jagan