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Introduction - 1 BACKGROUND QUANTUM PHYSICS 1900-1925 In...

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1 BACKGROUND QUANTUM PHYSICS 1900-1925 In these notes we briefly discuss several of the important developments in quantum physics in the period 1900-1925 before the invention of quantum mechanics by Heisenberg and Schrodinger [1, 2]. Blackbody radiation (Planck 1900) Consider the electromagnetic radiation inside a cavity with walls at temperature T , see Fig.1 . The energy is distributed across the frequency spectrum. Let U ( ν ) be the energy of radiation between frequency ν and ν + . Based on thermodynamics Wien predicted U ( ν ) = ν 3 f ( ν/T ) where f is an unknown function. ( ( ) I U Q Q , v FIG. 1. The intensity of light emitted at frequency ν is proportional to the corresponding energy density per unit frequency interval U ( ν ) in the cavity of volume V . Using classical elecromagnetic theory Rayleigh and Jeans found U ( ν ) = (8 πV/c 3 ) ν 2 kT ; at high frequencies this diverges as does the total energy integraltext 0 U ( ν ) . Wien fitted the measured distribution to the function U ( ν ) ν 3 e pν/ ( kT ) where k is Boltzmann’s constant and p is a numerically fitted parameter, though the fit was not very good. Planck obtained a perfect fit, within experimental error, to the measured spectrum with the function U ( ν ) = 8 πV c 3 3 1 e hν/ ( kT ) - 1 . The fitting parameter h = 6 . 6 × 10 34 Js is Planck’s constant. (Note: = planckover2pi1 ω where planckover2pi1 = h/ (2 π ) and ω = 2 πν .) Note that Planck’s law agrees with Wien’s law. Moreover it agrees with classical physics ( in the guise of the Rayleigh-Jeans law ) when kT >> hν (check it). Planck introduced the revolutionary “quantum hypothesis” that energy is emitted
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