## ABSTRACT

This Chapter develops the scalar quantum charged particle beam optics, applicable to spin-0 and spinless particles (i.e., particles for which the spin is ignored), based on the relativistic Klein-Gordon equation and the nonrelativistic Schrödinger equation. Normal magnetic quadrupole which focuses and defocuses the charged particle beam propagating along its straight optic axis simultaneously in perpendicular directions, axially symmetric magnetic lens used for focusing the beam in electron microscopes, and the dipole magnet used for bending the beam are studied using the formalism of scalar quantum charged particle beam optics. Quantum theory of image formation in an electron microscope is analysed. Axially symmetric electrostatic lens, electrostatic quadrupole, and the skew magnetic quadrupole are also studied. Effects of quantum uncertainties on the aberrations and nonlinear beam optics are discussed. Nonrelativistic approximation of the relativistic scalar quantum charged particle beam optics leads to the nonrelativistic scalar quantum charged particle beam optics based on the nonrelativistic Schrödinger equation.