Green's function methods for potential magnetic fields

Solar Physics ◽  
1982 ◽  
Vol 76 (2) ◽  
Author(s):  
Takashi Sakurai
Keyword(s):  
Magnetic Fields ◽  
Green’S Function ◽  
Green's Function

Retarded Green’s Functions

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Magnetic Fields ◽  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Impurity Scattering ◽  
Delta Function ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Dirac Delta

Chapter 5 introduces single-particle retarded Green’s functions, which provide the probability amplitude that a particle created at (x, t) is later annihilated at (x′,t′). Partial Green’s functions, which represent the time development of one (or a few) state(s) that may be understood as localized but are in interaction with a continuum of states, are discussed and applied to chemisorption. Introductions are also made to the Dyson integral equation, T-matrix and the Dirac delta-function potential, with the latter applied to random impurity scattering. The retarded Green’s function in the presence of random impurity scattering is exhibited in the Born and self-consistent Born approximations, with application to Ando’s semi-elliptic density of states for the 2D Landau-quantized electron-impurity system. Important retarded Green’s functions and their methods of derivation are discussed. These include Green’s functions for electrons in magnetic fields in both three dimensions and two dimensions, also a Hamilton equation-of-motion method for the determination of Green’s functions with application to a 2D saddle potential in a time-dependent electric field. Moreover, separable Hamiltonians and their product Green’s functions are discussed with application to a one-dimensional superlattice in axial electric and magnetic fields. Green’s function matching/joining techniques are introduced and applied to spatially varying mass (heterostructures) and non-local electrostatics (surface plasmons).

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