Dirac, c and a Supper date

doi:10.1016/j.ultramic.2020.112981

Ultramicroscopy

Volume 213, June 2020, 112981

https://doi.org/10.1016/j.ultramic.2020.112981 Get rights and content

Highlights

•
Relativistic electron optics.
•
Bodo von Borries.
•
Speed of light.
•
Last Supper.

Section snippets

Books

Equations are more important to me, because politics is for the present, but an equation is something for eternity
(Einstein)

Students of electron optics will know that almost all the books on the wave theory set out from Schrödinger's equation with at best a nod in the direction of Dirac. The volume on Quantum Mechanics of Charged Particle Beam Optics by R. Jagannathan and S.A. Khan is thus all the more remarkable in that the principal stages of electron optics are derived directly from Dirac's

Greener Grass

There was a young lady named Bright,

Whose speed was far faster than light;

She set out one day

In a relative way

And returned the previous night.
(Arthur Buller)

The authors of the two books noticed here are well known to electron microscopists. J.C.H. Spence is also fascinated by the history of attempts to measure the speed of light, catalyst of the theory of relativity. Lightspeed. The Ghostly Æther and the Race to Measure the Speed of Light [13] is the gripping account of his findings. (The

Conference proceedings

I have no more faith in men of science being infallible than I have of men of God being infallible, principally on account of them being men
(Noel Coward)

Every year, the annual meeting of the Japanese Society of Microscopy is recorded in full in a supplement to Kenbikyo. The majority of the abstracts are of course in Japanese but the titles and authors are translated and transliterated with the result that this supplement gives an excellent picture of microscopy research in Japan [15]. I can

Other and forthcoming

Her own mother lived the latter years of her life in the horrible suspicion that electricity was dripping all over the house
(James Thurber)

In Invariant Integrals in Physics [23], G.P. Cherepanov has brought together his many publications on the subject, which range from Flight and Adhesion to Cosmology via Fracking and Snow avalanches. I mention it here because it contains a chapter on ‘Relativistic electron beams’ but even this is far from electron optics for the electrons in question are

Declaration of Competing Interest

The author declares that he has no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Basic research is what I am doing when I don't know what I am doing
(Werner von Braun)

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References (26)

R. Jagannathan et al.
Quantum Mechanics of Charged Particle Beam Optics
(2019)
J.-L. Starck et al.
Sparse Image and Signal Processing, Wavelets and Related Geometric Multiscale Analysis
(2015)
G.J. Gbur
Singular Optics
(2017)
S. Samarin et al.
Spin-polarized Two-electron Spectroscopy of Surfaces
(2018)
J.C. Russ et al.
The Image Processing Handbook
(2016)
A Ul-Hamid
A Beginners’ Guide to Scanning Electron Microscopy
(2018)
F.H. Karrenberg
In the Light of the Electron Microscope, In the Shadow of the Nobel Prize, BOD–Books on Demand, Norderstedt
(2019)

J.C.H. Spence

Lightspeed, The Ghostly Æther and the Race to Measure the Speed of Light

(2019)

Cited by (13)

Quantum mechanics of bending of a charged particle beam by a dipole magnet
2024, Advances in Imaging and Electron Physics
Quantum mechanics of bending of a charged particle beam by a dipole magnet is studied in the paraxial approximation. Nonrelativistic quantum mechanics of the system is studied using the nonrelativistic Schrödinger equation ignoring the spin of the particle. To study the relativistic quantum mechanics of the system, ignoring the spin of the particle, the Klein–Gordon equation is used. Dirac equation is used to study the relativistic quantum mechanics of bending of a charged spin- $\frac{1}{2}$ particle beam by a dipole magnet. Classical theory of bending of a charged particle beam by a dipole magnet, in the paraxial approximation, is derived as an approximation of the quantum theory.
Anisotropic Airy beams
2023, Results in Optics
A matrix differential operator for passage from scalar to vector wave optics
2023, Results in Optics
One possible way to generalize scalar to wave optics, thus including polarization in the treatment consistent with the Maxwell equations was shown by Mukunda, Simon and Sudarshan (MSS) for paraxial systems, based on a group theoretical analysis. Later, the MSS theory for the passage from the Helmholtz scalar wave optics to the Maxwell vector wave optics was derived by casting the basic formalism in a framework very similar to the Dirac electron theory. Here, we show that the elegant MSS substitution rule is equivalent to a second-order 6 × 6 matrix differential operator for passage from scalar to vector wave optics. We explicitly obtained this matrix differential operator in a series and exponential forms respectively. Expressions for the electromagnetic field components are derived without making any assumptions on the form of the transverse beam profile. It is observed that all types of beams have certain characteristic relations among their field components. The power of the formalism is demonstrated by considering five specific beams.
Cross polarization in Gaussian and Bessel light beams
2023, Optics Communications
Quantum mechanics of round magnetic electron lenses with Glaser and power law models of B(z)
2021, Optik
Citation Excerpt :
Role of quantum uncertainties in the nonlinear part of the equations of motion for a nonparaxial beam, and in aberrations, has been pointed out. As remarked by Hawkes [87], quantum corrections to the classical theory of electron optics are ‘fortunately usually negligible’, and a long article by Majert and Kohl [88] on the simulation of atomically resolved elemental maps with a multislice algorithm for relativistic electrons shows that there are practical situations in which it is essential to use the Dirac theory. Thus, with the development of nano-level technology in future electron beam optical devices quantum effects may have to be considered seriously.
Scalar theory of quantum electron beam optics, at the single-particle level, derived from the Dirac equation using a Foldy–Wouthuysen-like transformation technique is considered. Round magnetic electron lenses with Glaser and power law models for the axial magnetic field $B (z)$ are studied. Paraxial quantum propagator for the Glaser model lens is obtained in terms of the well known fundamental solutions of its paraxial equation of motion. In the case of lenses with the power law model for $B (z)$ the well known fundamental solutions of the paraxial equations, obtained by solving the differential equation, are constructed using the Peano–Baker series also. Quantum mechanics of aberrations is discussed briefly. Role of quantum uncertainties in aberrations, and in the nonlinear part of the equations of motion for a nonparaxial beam, is pointed out. The main purpose of this article is to understand the quantum mechanics of electron beam optics though the influence of quantum effects on the optics of present-day electron beam devices might be negligible.
Classical and Quantum Mechanics of the Wien Velocity Filter
2024, International Journal of Theoretical Physics

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Dirac, c and a Supper date

Highlights

Section snippets

Books

Greener Grass

Conference proceedings

Other and forthcoming

Declaration of Competing Interest

First page preview

Quantum Mechanics of Charged Particle Beam Optics

Sparse Image and Signal Processing, Wavelets and Related Geometric Multiscale Analysis

Singular Optics

Spin-polarized Two-electron Spectroscopy of Surfaces

The Image Processing Handbook

A Beginners’ Guide to Scanning Electron Microscopy

In the Light of the Electron Microscope, In the Shadow of the Nobel Prize, BOD–Books on Demand, Norderstedt

Lightspeed, The Ghostly Æther and the Race to Measure the Speed of Light