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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 Planck’s constant, h, then the behavior of the system must be described within the framework of Quantum Mechanics . The Discovery of Planck’s 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 Planck’s constant and to the development of Quantum Mechanics!...
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