Abstract
To represent the wave function for the Schrödinger equation by a path integral raises the question of knowing if the path integral considered is well-defined. That is, given any potential V, is the associated oscillatory function path-integrable? This question is proved to be irrelevant regarding the semiclassical approximation problem. Indeed a probabilistic ansatz based on Wiener measure is exhibited, which under mild conditions on the potential, leads to the semiclassical approximation before the caustics. Such an anstaz is available after the caustics, but the link between this ansatz and the wave function is an open problem.
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© 1997 Springer Science+Business Media New York
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Castell, F. (1997). Semiclassical Approximation Using Wiener Measure. In: DeWitt-Morette, C., Cartier, P., Folacci, A. (eds) Functional Integration. NATO ASI Series, vol 361. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0319-8_17
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DOI: https://doi.org/10.1007/978-1-4899-0319-8_17
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-0321-1
Online ISBN: 978-1-4899-0319-8
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