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Nature Physics, 2006 Some of the next articles are maybe not open access.
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1988
An open subset D of ₵n is called pseudoconvex if −log d(z, CD) is plurisubharmonic. \(\left( {d\left( {z,CD} \right) = _{w \in CD}^{\inf }\left| {z - w} \right|} \right)\).
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An open subset D of ₵n is called pseudoconvex if −log d(z, CD) is plurisubharmonic. \(\left( {d\left( {z,CD} \right) = _{w \in CD}^{\inf }\left| {z - w} \right|} \right)\).
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1999
Green’s functions are named after the mathematician and physicist George Green who was born in Nottingham in 1793 and “invented” the Green’s function in 1828. This invention was developed in an essay written by Green entitled “Mathematical Analysis to the Theories of Electricity and Magnetism” originally published in Nottingham in 1828 and reprinted by
Peter D. Yardley +2 more
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Green’s functions are named after the mathematician and physicist George Green who was born in Nottingham in 1793 and “invented” the Green’s function in 1828. This invention was developed in an essay written by Green entitled “Mathematical Analysis to the Theories of Electricity and Magnetism” originally published in Nottingham in 1828 and reprinted by
Peter D. Yardley +2 more
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2016
In Chap. 2, Sect. 2.1.1, we considered one method, variation of parameters (or variation of constants ), for solving the linear inhomogeneous differential equation. In the method considered here, rather than determining the solution to the differential equation with the inhomogeneous term defined at each point of the interval, we consider the equation ...
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In Chap. 2, Sect. 2.1.1, we considered one method, variation of parameters (or variation of constants ), for solving the linear inhomogeneous differential equation. In the method considered here, rather than determining the solution to the differential equation with the inhomogeneous term defined at each point of the interval, we consider the equation ...
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2019
Green’s functions provide a simple and elegant way to solve differential equations, such as the wave equation in electrodynamics, and play an important role in nano optics. In this chapter we start by introducing the basic concepts of Green’s functions for the simplified scalar wave equation, and then ponder on the solutions of the full Maxwell’s ...
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Green’s functions provide a simple and elegant way to solve differential equations, such as the wave equation in electrodynamics, and play an important role in nano optics. In this chapter we start by introducing the basic concepts of Green’s functions for the simplified scalar wave equation, and then ponder on the solutions of the full Maxwell’s ...
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Contemporary Physics, 1968
Summary The motivation for the use of the Green's function (GF) concept in mathematical physics and the diversity of its applications are discussed, with reference to both classical and quantum mechanical problems. First, the impulse response GF is defined and its use is demonstrated in a problem in electrostatics. The connection with the wave response
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Summary The motivation for the use of the Green's function (GF) concept in mathematical physics and the diversity of its applications are discussed, with reference to both classical and quantum mechanical problems. First, the impulse response GF is defined and its use is demonstrated in a problem in electrostatics. The connection with the wave response
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2015
The solution of Helmholtz equation with a source term is faced, introducing the fundamental concept of Green’s function. The basic definitions and algebraic properties are reported, inverse and adjoint operators and eigenfunction expansions are introduced. For the important case of free space, the relevant boundary conditions at infinity are discussed,
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The solution of Helmholtz equation with a source term is faced, introducing the fundamental concept of Green’s function. The basic definitions and algebraic properties are reported, inverse and adjoint operators and eigenfunction expansions are introduced. For the important case of free space, the relevant boundary conditions at infinity are discussed,
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2004
In Chap. 7 we have found that all the S-matrix elements can be calculated once the correlation, or Green’s, functions are known. In this chapter we discuss how these functions can be obtained as functional derivatives of the generating functionals of the theory.
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In Chap. 7 we have found that all the S-matrix elements can be calculated once the correlation, or Green’s, functions are known. In this chapter we discuss how these functions can be obtained as functional derivatives of the generating functionals of the theory.
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