## Abstract

The theory of image formation for an electron microscope is based on the non-relativistic Schrodinger equation, whereas present-day electron microscopes operate with acceleration voltages of the order of one hundred to several hundreds of kilovolts, in which case relativistic effects become important. We present a fully relativistic theory of image formation, based on the appropriate Dirac equation. It is shown that, within certain approximations, always valid for today’s electron microscopes, a very simple expression for the current density can still be derived in terms of wave functions that are solutions to the relativistically covariant Klein-Gordon equation. The following paper presents the analysis of the often stated possibility to obtain the relativistically correct current density from the non-relativistic current density just by replacing the values of the non- relativistic momentum by the correct relativistic expression.

Original language | English |
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Pages (from-to) | 145-157 |

Number of pages | 13 |

Journal | Optica Acta |

Volume | 33 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Jan 1986 |

Externally published | Yes |