chapter3 - Chapter 3 Quantum Nature of Light and Matter We...

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Chapter 3 Quantum Nature of Light and Matter We understand classical mechanical motion of particles governed by New- ton’s law. In the last chapter we examined in some detail the wave nature of electromagnetic elds. We understand the occurance of guided traveling modes and of resonator modes. There are characteristic dispersion relations or resonance frequencies associated with that. In this chapter, we want to summarize some experimental ndings at the turn of the 19th century that ultimately lead to the discover of quantum mechanics, which is that matter has in addition to its particle like properties wave properties and electromag- netic waves have in addition to its wave properties particle like properties. As turns out the nal theory, which will be developed in subsequent chapters is much more than just that because the quantum mechanical wave function has a di f erent physical interpretation than a electromagnetic wave only the mathematical concepts used is in many cases very similar. However, this is a tremendous help and guideance in doing and nally understanding quantum mechanics. 3.1 Black Body Radiation In 1900 the physicist Max Planck found the law that governs the emission of electromagnetic radiation from a black body in thermal equilibrium. More speci cally Planck’s law gives the energy stored in the electromagntic eld in a unit volume and unit frequency range, [ f, f + df ] with df =1 Hz , when the 173
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CHAPTER 3. QUANTUM NATURE OF LIGHT AND MATTER electromagnetic eld is in thermal equilibrium with its surrounding that is at temperature T. A black body is simply de ned as an object that absorbs all light. The best implementation of a black body is the Ulbricht sphere, see Figure 3.1. Figure 3.1: The Ulbricht sphere, is a sphere with a small opening, where only a small amount of radiation can escape, so that the interior of the sphere is in thermal equilibrum with the walls, which are kept at a constant tremperature. The inside walls are typically made of di f use material, so that after multiple scattering of the walls any incoming ray is absorbed, i.e. the wall opening is black. Figure 3.2 shows the energy density w ( f ) of electromagnetic radiation in a black body at temperature T . Around the turn of the 19th century w ( f ) was measured with high precision and one was able to distinguish between various approximations that were presented by other researchers earlier, like the Rayleigh-Jeans law and Wien’s law, which turned out to be asymptotic approximations to Planck’s Law for low and high frequencies. In order to nd the formula describing the graphs shown in Figure 3.2 Planck had to introduce the hypothesis that harmonic oscillators with fre- quency f can not exchange arbitrary amounts of energy but rather only in discrete portions, so called quanta. Planck modelled atoms as classical oscillators with frequency f . Therefore, the energy of an oscillator must be quantized in energy levels corresponding
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chapter3 - Chapter 3 Quantum Nature of Light and Matter We...

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