arXiv subjects

Ramaswamy Jagannathan

Publications and source records attributed to Ramaswamy Jagannathan.

5 recordsLinked to original sources

arXiv2024

A new matrix representation of the Maxwell equations based on the Riemann-Silberstein-Weber vector for a linear inhomogeneous medium

We derive a new eight dimensional matrix representation of the Maxwell equations for a linear homogeneous medium and extend it to the case of a linear inhomogneous medium. This derivation starts ab initio with the Maxwell equations and uses arguments based on the algebra of the Pauli matrices. This process leads automatically to the matrix representation based on the Riemann-Silberstein-Weber (RSW) vector. The new representation for the homogeneous medium is a direct sum of four Pauli matrix blocks. This aspect of the new representation should make it suitable for studying the propagation of electromagnetic waves in a linear inhomogeneous medium adopting the techniques of quantum mechanics treating the inhomogeneity as a perturbation. The new representation is used to rederive the Mukunda-Simon-Sudarshan matrix substitution rule for transition from the Helmholtz scalar wave optics to the Maxwell vector wave optics.

math-ph↗

arXiv2021

Quantum mechanics of round magnetic electron lenses with Glaser and power law models of $B(z)$

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.

quant-ph↗

arXiv2020

On the deformed oscillator and the deformed derivative associated with the Tsallis q-exponential

The Tsallis $q$-exponential function $e_q(x) = (1+(1-q)x)^{\frac{1}{1-q}}$ is found to be associated with the deformed oscillator defined by the relations $\left[N,a^\dagger\right] = a^\dagger$, $[N,a] = -a$, and $\left[a,a^\dagger\right] = ϕ_T(N+1)-ϕ_T(N)$, with $ϕ_T(N) = N/(1+(q-1)(N-1))$. In a Bargmann-like representation of this deformed oscillator the annihilation operator $a$ corresponds to a deformed derivative with the Tsallis $q$-exponential functions as its eigenfunctions, and the Tsallis $q$-exponential functions become the coherent states of the deformed oscillator. When $q = 2$ these deformed oscillator coherent states correspond to states known variously as phase coherent states, harmonious states, or pseudothermal states. Further, when $q = 1$ this deformed oscillator is a canonical boson oscillator, when $1 < q < 2$ its ground state energy is same as for a boson and the excited energy levels lie in a band of finite width, and when $q \longrightarrow 2$ it becomes a two-level system with a nondegenerate ground state and an infinitely degenerate excited state.

math-ph↗

arXiv2019

Quantum mechanics of bending of a nonrelativistic charged particle beam by a dipole magnet

Quantum mechanics of bending of a nonrelativistic monoenergetic charged particle beam by a dipole magnet is studied in the paraxial approximation. The transfer map for the position and momentum components of a particle of the beam between two transverse planes at different points on the curved optic axis of the system is derived starting with the nonrelativistic Schrödinger equation. It is found that the quantum transfer map contains the classical transfer map as the main part and there are tiny quantum correction terms. The negligibly small quantum corrections explain the remarkable success of classical mechanics in charged particle beam optics.

quant-ph↗

arXiv2002

Foldy-Wouthuysen transformation and a quasiparaxial approximation scheme for the scalar wave theory of light beams

The Foldy-Wouthuysen iterative diagonalization technique is applied to the Helmholtz equation to obtain a Hamiltonian description of the propagation of a monochromatic quasiparaxial light beam through a system in which the refractive index $n(x,y,z)$ varies about a background value $n_0$ such that $|n(x,y,z)-n_0| \ll n_0$. This technique is presented as an alternative to the conventional method of series expansion of the radical. Besides reproducing all the traditional quasiparaxial terms, this method leads to additional terms in the optical Hamiltonian.

physics.optics↗