Chapter3_1 - which has dimensions of action assumes a...

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PHY3063 R. D. Field Department of Physics Chapter3_1.doc University of Florida In Search of a Missing Fundamental Constant In the theory of relativity the constant c plays a fundamental role: β = v/c << 1 (non-relativistic “classical” physics holds) β = v/c 1 (must use relativity) Question: Does an analogous criterion exist which tells us when we must apply quantum mechanics and when the “classical” theory is okay? Answer: Yes! Planck’s constant. s eV s J h × = × = 15 34 10 136 . 4 10 626 . 6 The dimensions of Planck’s constant are [energy]×[time]= [length]×[momentum]= [angular momentum]= [ “action” ] Criterion: If for a physical system any “natural” dynamical variable
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Unformatted text preview: which has dimensions of action assumes a numerical value comparable to Plancks constant, h, then the behavior of the system must be described within the framework of Quantum Mechanics . The Discovery of Plancks Constant Outstanding problems at the beginning of the century: (a) The problem of black-body radiation. (b) The problem of the photoelectric effect. (c) The problem of the stability of the size of atoms. (d) Compton scattering. The missing constant! It is small! Studying these problems led to the discovery of Plancks constant and to the development of Quantum Mechanics!...
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This note was uploaded on 05/29/2011 for the course PHY 3063 taught by Professor Field during the Spring '07 term at University of Florida.

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