Theory of Perturbations
The number of calculations that can be carried out exactly, either in classical or in quantum dynamics, is comparatively small and the number of useful results so obtained is even smaller. The greater part of physics, engineering, and dynamical astronomy involves approximations, and the worst difficulties arise when the variables of a problem are not separable. What one hopes to do is to find a corresponding problem in which not only are the variables separable but the resulting differential equations can be solved exactly, and then move from the solved problem to the unsolved one by a systematic procedure of approximation, usually involving expansion in series. The procedures in quantum and in classical mechanics can be carried out in somewhat analogous fashions, but there is no use in pursuing the comparison very far since what is observable differs in the two theories. An astronomer, for example, wishes to calculate positions in the sky and has little interest in knowing energies, whereas in atomic physics an electron’s position is not an observable while its energy is.
KeywordsQuantum Mechanic Anharmonic Oscillator Unperturbed System Unperturbed State Unperturbed Problem
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