AFLS2025

Quantum Mechanical Formalism of Charged-Particle Beam Optics

20 Nov 2025, 09:15

15m

AfPS Thursday Morning I

Speaker

Prof. Sameen Ahmed Khan (Department of Mathematics and Sciences, College of Arts and Applied Sciences, Dhofar University)

Description

Quantum Mechanical Formalism of Charged-Particle Beam Optics

Sameen Ahmed Khan

Department of Mathematics and Sciences, College of Arts and Applied Sciences, Dhofar University, Salalah, Sultanate of Oman.
rohelakhan@yahoo.com, http://orcid.org/0000-0003-1264-2302

A formalism of Quantum Charged Particle Beam Optics is being developed since 1989 for both nonrelativistic and relativistic situations based on the nonrelativistic Schrödinger equation, Klein-Gordon equation, and the Dirac equation. This article gives glimpses of the basic framework of this formalism with the examples of round magnetic lens. This formalism has further led to quantum methodologies for treating light beam optics including polarization. The use of quantum methodologies results in an elegant 6×6 matrix differential operator for transition from the Helmholtz scalar wave optics to the Maxwell vector wave optics. We explicitly obtained this matrix differential operator in a series and exponential form respectively. The operator works for all types of light beams and its action is demonstrated to obtain the cross polarization in Gaussian light beams.

Keywords: Quantum Mechanics, Charged Particle Beam Optics; Light Polarization.

References

1. R. Jagannathan and S. A. Khan, Quantum theory of the optics of charged particles, Chapter-4 in Advances in Imaging and Electron Physics, 97, 257-358 (1996); http://dx.doi.org/10.1016/S1076-5670(08)70096-X.

2. R. Jagannathan and S. A. Khan, Quantum Mechanics of Charged Particle Beam Optics: Understanding Devices from Electron Microscopes to Particle Accelerators, 356 pages, CRC Press, Taylor & Francis (2019); https://doi.org/10.1201/9781315232515.

3. S. A. Khan and R. Jagannathan, Quantum mechanics of bending of a charged particle beam by a dipole magnet, Advances in Imaging and Electron Physics, 229, 1-41 (2024); https://doi.org/10.1016/bs.aiep.2024.02.001.

4. S. A. Khan, Passage from scalar to vector optics and the Mukunda-Simon-Sudarshan theory for paraxial systems, Journal of Modern Optics, 63 (17), 1652-1660 (2016); http://dx.doi.org/10.1080/09500340.2016.1164257.

5. S. A. Khan, Quantum Methods in Light-Beam Optics, Optics & Photonics News (OPN), 27 (12), 47 (2016); https://doi.org/10.1364/OPN.27.12.000047. One of the thirty papers selected under the theme, Optics in 2016, highlighting the most exciting peer-reviewed optics research to have emerged over the past 12 months.

6. S. A. Khan, Hamilton’s Optical-Mechanical Analogy in the Wavelength-dependent Regime, Optik, 130C, 714-722 (2017); http://dx.doi.org/10.1016/j.ijleo.2016.10.112.

7. S. A. Khan, The Foldy-Wouthuysen Transformation Technique in Optics, Advances in Imaging and Electron Physics, 152, 49-78 (2008); http://dx.doi.org/10.1016/S1076-5670(08)00602-2.

8. S. A. Khan and R. Jagannathan, A new matrix representation of the Maxwell equations based on the Riemann-Silberstein-Weber vector for a linear inhomogeneous medium, Results in Optics, 17, 100747 (2024); https://doi.org/10.1016/j.rio.2024.100747.

9. S. A. Khan, A Matrix Differential Operator for Passage from Scalar to Vector Optics, Results in Optics, 13, 100527 (2023); https://doi.org/10.1016/j.rio.2023.100527.

10. S. A. Khan, Anisotropic Airy beams, Results in Optics, 13, 100569 (2023); https://doi.org/10.1016/j.rio.2023.100569.

11. S. A. Khan and R. Jagannathan, Matrix formalism of Maxwell light beam optics including polarization, Advances in Imaging and Electron Physics, 235, 1-111 (2025); https://doi.org/10.1016/bs.aiep.2025.06.002.