Frequency-dependent multipole polarizabilities and reduced Green’s functions. I. The ground state hydrogen atom

1977 ◽  
Vol 67 (5) ◽  
pp. 1799 ◽  
Author(s):  
Keith McDowell
Keyword(s):  
Hydrogen Atom ◽  
Ground State ◽  
Green's Functions ◽  
Green’S Functions ◽  
Frequency Dependent

scholarly journals Renormalized spectrum of quasiparticle in limited number of states, strongly interacting with two-mode polarization phonons at T=0 K

2021 ◽  
Vol 24 (1) ◽  
pp. 13705
Author(s):  
M.V. Tkach ◽  
Ju.O. Seti ◽  
O.M. Voitsekhivska
Keyword(s):  
Energy Spectrum ◽  
Ground State ◽  
Green's Functions ◽  
Green’S Functions ◽  
Phonon Modes ◽  
Strongly Interacting ◽  
Renormalized Energy ◽  
Initial States ◽  
Analytical Expressions

Within unitary transformed Hamiltonian of Fröhlich type, using the Green's functions method, exact renormalized energy spectrum of quasiparticle strongly interacting with two-mode polarization phonons is obtained at T=0 K in a model of the system with limited number of its initial states. Exact analytical expressions for the average number of phonons in ground state and in all satellite states of the system are presented. Their dependences on a magnitude of interaction between quasiparticle and both phonon modes are analyzed.

scholarly journals Eigenvalues, eigenfunctions and Green's functions on a path via Chebyshev polynomials

2009 ◽  
Vol 3 (2) ◽  
pp. 282-302 ◽  
Author(s):  
E. Bendito ◽  
A.M. Encinas ◽  
A. Carmona
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Poisson Equation ◽  
Chebyshev Polynomials ◽  
Ground State ◽  
Green's Functions ◽  
Periodic Boundary ◽  
Green’S Functions ◽  
Boundary Value ◽  
The Poisson Equation

In this work we analyze the boundary value problems on a path associated with Schr?dinger operators with constant ground state. These problems include the cases in which the boundary has two, one or none vertices. In addition, we study the periodic boundary value problem that corresponds to the Poisson equation in a cycle. Moreover, we obtain the Green's function for each regular problem and the eigenvalues and their corresponding eigenfunctions otherwise. In each case, the Green's functions, the eigenvalues and the eigenfunctions are given in terms of first, second and third kind Chebyshev polynomials.

Temperature field evaluation of a two-dimensional partial heat flow problem through Green's Functions

2019 ◽  
Author(s):  
Guilherme Ramalho Costa ◽  
José Aguiar santos junior ◽  
José Ricardo Ferreira Oliveira ◽  
Jefferson Gomes do Nascimento ◽  
Gilmar Guimaraes
Keyword(s):  
Temperature Field ◽  
Heat Flow ◽  
Green's Functions ◽  
Flow Problem ◽  
Green’S Functions ◽  
Field Evaluation ◽  
Two Dimensional
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