Fully relativistic treatment of electron-optical image formation based on the dirac equation

H.A. Ferwerda, B.J. Hoenders, C.H. Slump

Research output: Contribution to journalArticleAcademicpeer-review

15 Citations (Scopus)
24 Downloads (Pure)

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 languageEnglish
Pages (from-to)145-157
Number of pages13
JournalOptica Acta
Volume33
Issue number2
DOIs
Publication statusPublished - 1 Jan 1986
Externally publishedYes

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