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

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

doi:10.1080/713821923

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

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

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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
Pages (from-to)	145-157
Number of pages	13
Journal	Optica Acta
Volume	33
Issue number	2
DOIs	https://doi.org/10.1080/713821923
Publication status	Published - 1 Jan 1986
Externally published	Yes

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title = "Fully relativistic treatment of electron-optical image formation based on the dirac equation",

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{\textquoteright}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.",

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N2 - 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.

AB - 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.

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

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