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

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Unformatted text preview: 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 ( ) d be the energy of radiation between frequency and + d . Based on thermodynamics Wien predicted U ( ) = 3 f ( /T ) where f is an unknown function. ( ( ) I U Q Q , v FIG. 1. The intensity of light emitted at frequency is proportional to the corresponding energy density per unit frequency interval U ( ) in the cavity of volume V . Using classical elecromagnetic theory Rayleigh and Jeans found U ( ) = (8 V/c 3 ) 2 kT ; at high frequencies this diverges as does the total energy integraltext U ( ) d . Wien fitted the measured distribution to the function U ( ) 3 e p/ ( kT ) where k is Boltzmanns 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 ( ) = 8 V c 3 h 3 1 e h/ ( kT )- 1 . The fitting parameter h = 6 . 6 10 34 Js is Plancks constant. (Note: h = planckover2pi1 where planckover2pi1 = h/ (2 ) and = 2 .) Note that Plancks law agrees with Wiens law. Moreover it agrees with classical physics ( in the guise of the Rayleigh-Jeans law ) when kT >> h (check it). Planck introduced the revolutionary quantum hypothesis that energy is emitted(check it)....
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This note was uploaded on 01/22/2012 for the course PHYS 3143 taught by Professor Kennedy during the Fall '10 term at Georgia Institute of Technology.

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

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