Download Semiclassical approximations in wave mechanics by Berry M.V., Mount K.E. PDF

By Berry M.V., Mount K.E.

We evaluate quite a few tools of deriving expressions for quantum-mechanical amounts within the restrict whilst % is small (in comparability with the appropriate classical motion functions). first of all we deal with one-dimensional difficulties and talk about the derivation of WKB connection formulae (and their reversibility), mirrored image coefficients, section shifts, sure kingdom standards and resonance formulae, using first the complicated approach during which the classical turning issues are kept away from, and secondly the strategy of comparability equations because of which uniform approximations are derived, that are legitimate during the turning-point areas. The detailed difficulties linked to radial equations also are thought of. subsequent we research semiclassical power scattering, either for its personal sake and in addition for example of the three-stage approximation technique which needs to commonly be hired whilst facing eigenfunction expansions below semi-classical stipulations, once they converge very slowly. eventually, we speak about the derivation of semiclassical expressions for eco-friendly services and effort point densities in very normal situations, using Feynman's path-integral procedure and

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327-8) While causality is an 'age-old way of thinking of all mankind', it is not a logical necessity, and von Neumann did not believe that it was reasonable to sacrifice a physical theory that made such good empirical predictions for its sake (328). While he granted that quantum mechanics was a troubled theory, since there was nothing better to put in its place, and since any change that would make it more intuitive would require a very different theory, he considered his job to be to try to make sense of the theory that the physicists had developed so far.

Rather, I shall describe what Everett himself said in considerable detail, then focus on a few of the more influential criticisms and reconstructions of his position and compare and contrast some of the problems and virtues of each of these. Throughout I shall try to provide ample evidence of what people have actually said. If nothing else, I hope that this will help to sharpen the various debates involving Everett's relative-state theory by pointing out some of the ambiguities that must be resolved before a sensible discussion can even get started.

While von Neumann assumed for the purposes of his work that everything that can be said about the state of a physical system must be derived from the vector that represents its state, contrary to popular wisdom he did not believe that the standard quantum-mechanical state was necessarily complete. Rather, he thought that the principle of state completeness, the standard interpretation of states, and the acausal nature of quantum mechanics might ultimately prove to be provisional features of quantum mechanics.

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