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ls2_unit_4 - THE INTERACTION OF RADIATION AND MATTER...

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T HE I NTERACTION OF R ADIATION AND M ATTER : S EMICLASSICAL T HEORY P AGE 38 R. Victor Jones, March 9, 2000 IV. R EVIEW OF B ASIC Q UANTUM M ECHANICS : T HE T HERMAL R ADIATION F IELD P LANCK ' S R ADIATION L AW FOR T HERMAL S OURCES : 16 To set the stage for subsequent discussions of laser physics and quantization of the electromagnetic field we briefly explore the earliest, seminal notions in the quantum theory of light. As we all remember, in 1900 Planck found that he could account for the measured spectral distribution of radiation from a thermal source by postulating that the energies of a certain set of harmonic oscillators are quantized! Drawing on Planck's success, Einstein in 1905 was able to show that the extraordinary features of photoelectric effect could be explained by hypothesizing the corpuscularity of the electromagnetic field. The crowning triumph of early quantum optics is Einstein's amazingly simple, phenomenological theory of 1917 which provided a quantitative basis for analyzing the absorption and emission of light by atoms. In treating thermal sources the basic assumption is that emitted radiation is a sample of the total electromagnetic field -- viz. all of the modes of a resonator -- in thermal equilibrium with its material environment -- viz. the walls of the resonator. In the traditional treatment of the theory of black-body radiation , a particular thermodynamic system is assumed - - viz. , a hollow resonator which is a cube of length L with has perfectly conducting walls. 17 Thus, to satisfy boundary conditions at the walls, the electric field associated with a particular mode of the cavity is given by 16 This section and some parts of the following section draw heavily upon discussions in Rodney Loudon's The Quantum Theory of Light (2nd edition), Oxford (1983). 17 The detail results of black-body radiation theory are indeed sensitive to the assumed character of the thermodynamic systemas will be demonstration presently.
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T HE I NTERACTION OF R ADIATION AND M ATTER : S EMICLASSICAL T HEORY P AGE 39 R. Victor Jones, March 9, 2000 E x ν x , ν y , ν z r r , t ( 29 = E x 0 k ν x , ν y , ν z ( 29 cos π ν x x L ( 29 sin π ν y y L ( 29 sin π ν z z L ( 29 exp i ϖ ν x ν y ν z t ( 29 E y ν x , ν y , ν z r r , t ( 29 = E y 0 k ν x , ν y , ν z ( 29 sin π ν x x L ( 29 cos π ν y y L ( 29 sin π ν z z L
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