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Greens Functions in Mathematical Physios
TimeDependent Greens Functions
Physical Significance of G Application to the Free Particle Case
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analytic continuation approximation band edge behavior Bethe lattice boundary conditions branch cut Brillouin zone calculate causal Green's function continuous spectrum continuum contribution corresponding defined denotes density diagonal matrix diagonal matrix element diagrams discontinuity discrete level disordered system eigenenergies eigenfrequency eigenfunctions eigenstates eigenvalues electrons expressed in terms Fermi surface Fermi system fermions finite follows Fourier transform free particle g's and g's given Green's function hamiltonian Heisenberg picture Hence imaginary impurity infinite integral limit localized eigenstates nearest neighbors noninteracting normal obeyed obtain path perturbation expansion phonons Phys plane poles potential probability amplitude quantity quantum quasi-particle r-representation real w-axis relation resonance result satisfies scattering amplitude Schrödinger Schrödinger equation simple singularities solid-state solution spectrum of H Substituting summation t-matrix Taking into account terms of g theorem theory ticle tight binding hamiltonian tion total hamiltonian unit volume unperturbed values variables various g's vertex wave equation zero