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Green‘s Functions in Quantum Physics978-3-540-28841-1Series ISSN 0171-1873 Series E-ISSN 2197-4179

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https://doi.org/10.1007/978-3-663-14577-6In this chapter, the time-independent Green’s functions are defined, their main properties are presented, methods for their calculation are briefly discussed, and their use in problems of physical interest is summarized.

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https://doi.org/10.1007/978-3-663-08810-3The Green’s functions corresponding to linear partial differential equations of first and second order in time are defined; their main properties and uses are presented.

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Time-Dependent Green’s FunctionsThe Green’s functions corresponding to linear partial differential equations of first and second order in time are defined; their main properties and uses are presented.

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Physical Significance of ,. Application to the Free-Particle CaseThe general theory developed in Chap. 1 can be applied directly to the time-independent one-particle Schr?dinger equation by making the substitutions .(.)→?(.), λ → ., where ?(.) is the Hamiltonian. The formalism presented in Chap. 2, Sects. 2.1,2.2 is applicable to the time-dependent one-particle Schr?dinger equation.

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Auftragsplanung und -steuerung,nctions like the conductivity. The poles of an appropriate analytic continuation of . in the complex .-plane can be interpreted as the energy (the real part of the pole) and the inverse lifetime (the imaginary part of the pole) of quasiparticles. The latter are entities that allow us to map an interacting system to a noninteracting one.