introqm - Quantum Mechanics: Discretization of Energy and...

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Quantum Mechanics: Discretization of Energy and Wave-Particle Duality 15th March 2010 1 Introduction Classical physics (derived from the ideas of Newton, Hamilton, Lagrange and other early physicists) encountered several experimental observations that it could not fully resolve within its formalisms and constructs. This occurred during the turn of the 20th century. Here we brieFy discuss the canonical historical experiments that led to the understanding of the discrete nature of energies of matter at the atomic level, as well as the wave-particle duality of matter on the same lengthscales. 2 Blackbody Radiation and the UV Catastrophe We know intuitively that objects at a particular temperature radiate elec- tromagnetic (em) energy; we emphasize that the energy is not just in the visible range of the em spectrum, but spans, in theory, the entire range. Consider a space heater, glowing embers of a ±re, glowing charcoal embers, an incandescent light bulb, a kitchen oven, etc. In each case, we know in- tuitively that there is associated some radiation of energy corresponding to the temperature of the body (we can feel the heat around each of the bodies mentioned). An idealization of these types of systems is the black body emitter. The black body emits radiation that is in thermal equilibrium at the temperature of the body. We can now speak of the spectral density of the body. The spectral density is the energy stored in the em feld oF the blackbody emitter at Frequency ν per unit volume and unit Frequency . ρ ( ν, T ) = 8 π ν 2 c 3 h E oscillator i The total energy per unit volume in a small range of frequencies is 1
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ρ ( ν, T ) = 8 π ν 2 c 3 h E oscillator i The origin of the black body emitter’s energy is taken to be from the oscil- latory
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This note was uploaded on 05/10/2011 for the course CHEM 444 taught by Professor Dybowski,c during the Spring '08 term at University of Delaware.

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introqm - Quantum Mechanics: Discretization of Energy and...

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