ls2_unit_1 - THE INTERACTION OF RADIATION AND MATTER : S...

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T HE I NTERACTION OF R ADIATION AND M ATTER : S EMICLASSICAL T HEORY I. R EVIEW OF B ASIC Q UANTUM M ECHANICS : C ONCEPTS , P OSTULATES AND N OTATION : At the outset, let us, briefly, reconsider why quantum mechanics is necessary? Forces known in classical electrodynamics cannot account for the remarkable stability of atoms and molecules. Disturbed dynamic systems radiate only frequencies which may be expressed as differences between certain values (Ritz's Combination Law of Spectroscopy). 1 All physical systems -- viz. material "particles" and electromagnetic fields -- exhibit wave-particle duality -- i.e. to explain particular observations the system must in some instances be modeled as a particle and in others as a wave. There is a limit below which the disturbance associated with a observation is not negligible and, thus, there is an unavoidable indeterminacy in the prediction of observed results. To proceed, we recall an ancient comment of P. A. M. Dirac: 2 "Quantum mechanics…requires the states of a dynamic system and the dynamical variables to be to be interconnected in quite strange ways that are unintelligible from the classical standpoint. The states and dynamic variables have to be represented by mathematical quantities of different natures from those ordinarily used in physics" Following the Master we begin with the general quantum mechanical principle of superposition of states . To quote him once more: 1 According to classical theory, a disturbed system should radiate certain fundamental frequencies and their harmonics. Each fundamental frequency would be associated with one of the systems degrees of freedom. 2 P. A. M. Dirac, The Principles of Quantum Mechanics (Revised fourth edition), Oxford University Press (1967).
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THE INTERACTION OF RADIATION AND MATTER: SEMICLASSICAL THEORY PAGE 2 R. Victor Jones, March 6, 2000 "The non-classical nature of the superposition process is brought out clearly if we consider the superposition of two states, A and B, such that there exists an observation which, when made on the system in state A, is certain to lead to one particular result, a say, and when made on the system in state B is certain to lead to some different result, b say. What will be the result of the observation when made on the system in the superposed state? The answer is that the result will be sometimes a and sometimes b , according to a probability law depending on the relative weights of A and B in the superposition process. It will never be different from both a and b . The intermediate character of the state formed by superposition thus expresses itself through the probability of a particular result for an observation being intermediate between the corresponding probabilities for the original states, not through the result itself being intermediate between the corresponding results for the original states . "…The superposition process is a kind of additive process and implies that states
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This note was uploaded on 01/31/2011 for the course PHYSICS 108 taught by Professor Staff during the Winter '08 term at UC Davis.

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ls2_unit_1 - THE INTERACTION OF RADIATION AND MATTER : S...

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