Quantum Description of Electromagnetic Waves in Time-Dependent Linear Media

The formal mathematical analogy between time-dependent quantum equation for the nonrelativistic particles and time-dependent equation for the propagation of electromagnetic waves had been studied in [A. I. Akhiezer and V. B. Berestezki, Quantum Electrodynamics (FM, Moscow, 1959) [in Russian] and S. Schweber, An Introduction to Relativistic Quantum Field Theory, Chap. 5.3 (Row, Peterson & Co, Ill, 1961)]. Here, we deal with the time-dependent Schrödinger equation for nonrelativistic particles and with time-dependent Helmholtz equation for electromagnetic waves. Then, using this similarity, the tunneling and multiple internal reflections in one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) particle and photon tunneling are studied. Finally, some conclusions and future perspectives for further investigations are presented.

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Non-linear cross modulation of electromagnetic waves in a plasma due to time-dependent electron density

Journal of Physics D Applied Physics ◽

10.1088/0022-3727/1/1/309 ◽

1968 ◽

Vol 1 (1) ◽

pp. 55-62 ◽

Cited By ~ 1

Author(s):

M S Sodha ◽

B K Sawhney

Keyword(s):

Electron Density ◽

Electromagnetic Waves ◽

Time Dependent ◽

Cross Modulation ◽

Non Linear

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Квадрупольное излучение незаряженной капли, осциллирующей в однородном электростатическом поле

Журнал технической физики ◽

10.21883/jtf.2019.03.47169.147-18 ◽

2019 ◽

Vol 89 (3) ◽

pp. 360

Author(s):

А.И. Григорьев ◽

С.О. Ширяева ◽

Н.Ю. Колбнева

Keyword(s):

Mathematical Model ◽

Electromagnetic Waves ◽

Oscillation Amplitude ◽

Electric Quadrupole ◽

Time Dependent ◽

Linear Size ◽

Uniform Electric Field ◽

Radiation Wavelength ◽

Electric Quadrupole Moment ◽

First Order

AbstractCapillary oscillations of an uncharged spheroid droplet of nonviscous conducting uncompressible liquid in the presence of uniform electric field are analyzed in the first order of smallness with respect to the ratio of the oscillation amplitude to a linear size of the droplet and in the second order of smallness with respect to the squared ratio of the linear size to the radiation wavelength. It is shown that the electric quadrupole moment of the droplet is time-dependent due to surface oscillations, which lead to the emission of quadrupole electromagnetic waves. A mathematical model of the quadrupole electromagnetic radiation of an uncharged droplet that oscillates in the presence of electrostatic field is constructed, and the radiation intensity and frequency are estimated.

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