Abstract
The importance of the evolution operator in quantum mechanics has been emphasized several times. We now obtain an explicit formula for its matrix elements in terms of a path integral. Next we evaluate that integral in the semiclassical case, that is, when the action associated with the classical trajectory is much larger than Planck’s constant. This will lead to an approximation for the eigenvalues and eigenfunctions of the Hamiltonian of a particle in one dimension, valid for high energy levels. The relation between quantum and classical properties will also be investigated more closely.
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© 2002 Springer-Verlag Berlin Heidelberg
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Marchildon, L. (2002). The Path Integral. In: Quantum Mechanics. Advanced Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04750-7_16
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DOI: https://doi.org/10.1007/978-3-662-04750-7_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07767-8
Online ISBN: 978-3-662-04750-7
eBook Packages: Springer Book Archive