Precise theory of the Stark effect on hydrogen- and helium-like atoms

2002 ◽  
Vol 80 (11) ◽  
pp. 1401-1412 ◽  
Author(s):  
V D Ovsiannikov ◽  
V G Pal'chikov
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Ground State ◽  
Stark Effect ◽  
Energy Levels ◽  
Relativistic Effects ◽  
Model Potential ◽  
Matrix Elements ◽  
Angular Momenta ◽  
Relativistic Coulomb

The relativistic effects on the dipole polarizabilities and hyperpolarizabilities are considered for different kinds of energy levels in hydrogen- and helium-like atoms. The relativistic Coulomb Green's function is used for calculating the susceptibilities of the ground-state hydrogen up to terms of order (α Z)10. Both relativistic and interelectronic corrections are determined for the ground state of helium. The formulas are given for polarizability and hyperpolarizability in the relativistic "screened-charge" approximation. The anticrossing of the triplet 3PJ states with zero magnetic quantum number is studied on the basis of perturbation theory for degenerate states. General expressions are given for the dipole matrix elements, up to the fourth order in field strength, within the basis of close fine-structure substates with equal angular momenta L and different total momenta J. The calculation of the higher order matrix elements is carried out with the use of the Green's function in the model potential approximation. PACS Nos.: 31.10Dk, 31.15Ar, 31.30Jv, 32.10-f, 31.25Eb

Particle with a time-dependent mass in the Coulomb and the inverse quadratic potentials

2018 ◽  
Vol 15 (04) ◽  
pp. 1850057
Author(s):  
Badri Berrabah ◽  
Baya Bentag ◽  
Ahmida Bendjoudi
Keyword(s):  
Charged Particle ◽  
Green’S Function ◽  
Green's Function ◽  
Bound States ◽  
Energy Levels ◽  
Wave Functions ◽  
Time Dependent ◽  
Quadratic Potentials ◽  
Dependent Mass

The problem of a spineless charged particle with a time-dependent decaying mass interacting with a Coulomb and an inverse quadratic potentials is considered. The Green’s function is explicitly evaluated. The energy levels as well as the wave functions for the bound states are exactly determined.

INVERSE FORMULATION OF THE GREEN'S FUNCTION THEORY: EXACT SOLUTION FOR THE BETHE LATTICE

2001 ◽  
Vol 15 (21) ◽  
pp. 2935-2943 ◽  
Author(s):  
L. ŠAMAJ
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Nearest Neighbor ◽  
Tight Binding ◽  
Bethe Lattice ◽  
Diagonal Matrix ◽  
Local Form ◽  
Matrix Elements ◽  
Factorization Property ◽  
Inverse Form

We study the tight-binding Hamiltonian H=∑j|j> ∊j<j| + ∑j,k |j>Vjk < k | defined on the Bethe lattice of an arbitrary coordination number; the hopping elements Vjk are nonzero (and constant) only for j,k being the nearest-neighbor sites and the energies ∊j are considered to be site-dependent. The Green's function (z-H)-1 problem is solved explicitly in the inverse form, with diagonal matrix elements {<j | (z-H)-1 | j >} as controlling (prescribed) variables. Namely: (i) the inverse profile relation, i.e. z-∊j versus diagonal matrix elements, is obtained in a local form; (ii) the off-diagonal matrix elements { <j | (z-H)-1 | k >} are shown to exhibit a simple factorization property in terms of the diagonal ones.

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