Quantum mechanics of round magnetic electron lenses with Glaser and power law models of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e26" altimg="si3.svg"><mml:mrow><mml:mi>B</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>

Scalar theory of quantum electron beam optics, at the single-particle level, derived from Dirac equation using a Foldy–Wouthuysen-like transformation technique is considered. Round magnetic lenses with Glaser and power law models for axial field B(z) are studied. Paraxial propagator model lens obtained in terms well known fundamental solutions its paraxial motion. In case equations, by solving differential equation, constructed Peano–Baker series also. Quantum mechanics aberrations discussed briefly. Role uncertainties aberrations, nonlinear part equations motion nonparaxial beam, pointed out. The main purpose this article to understand optics though influence effects on present-day devices might be negligible.