Titlebook: Classical and Quantum Dynamics; From Classical Paths Walter Dittrich,Martin Reuter Textbook 20013rd edition Springer-Verlag Berlin Heidelbe

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Vladimir Estivill-Castrol,Alan T. Murray, ..) is the generator of a canonical transformation to new constant momenta .., (all .., are ignorable), and the new Hamiltonian depends only on the ..,: . = . = .(..). Besides, the following canonical equations are valid:

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https://doi.org/10.1007/978-3-0348-6686-6 conservative, ∂./∂. = 0, and periodic in both the unperturbed and perturbed case. In addition to periodicity, we shall require the Hamilton-Jacobi equation to be separable for the unperturbed situation. The unperturbed problem ..(..) which is described by the action-angle variables .. and .. will b

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https://doi.org/10.1007/978-3-642-85278-7dimensional surface. If we then consider the trajectory in phase space, we are interested primarily in its piercing points through this surface. This piercing can occur repeatedly in the same direction. If the motion of the trajectory is determined by the Hamiltonian equations, then the . + 1-th pie

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Outlook in the Field of Deck Bridges,tablish the formal connection between operator and path integral formalism. Our objective is to introduce the generating functional into quantum mechanics. Naturally we want to generate transistion amplitudes. The problem confronting us is how to transcribe operator quantum mechanics as expressed in

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Jacobi Fields, Conjugate Points,particular, we want to investigate the conditions under which a path is a minimum of the action and those under which it is merely an extremum. For illustrative purposes we consider a particle in two-dimensional real space. If we parametrize the path between points . and . by ϑ, then Jacobi’s principle states:

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Removal of Resonances,rs appear in the expression for the adiabatic invariants. We now wish to begin to locally remove such resonances by trying, with the help of a canonical transformation, to go to a coordinate system which rotates with the resonant frequency.