Symbolic Algorithms of Algebraic Perturbation Theory: Hydrogen Atom in the Field of Distant Charge

2001 ◽  
pp. 309-322
Author(s):  
Alexander Gusev ◽  
Valentin Samoilov ◽  
Vitaly Rostovtsev ◽  
Sergue Vinitsky
Keyword(s):  
Perturbation Theory ◽  
Hydrogen Atom ◽  
Symbolic Algorithms

Symbolic Algorithms of Algebraic Perturbation Theory for a Hydrogen Atom: the Stark Effect

2000 ◽  
pp. 219-231 ◽  
Author(s):  
Alexander Gusev ◽  
Valentin Samoilov ◽  
Vitaly Rostovtsev ◽  
Sergue Vinitsky
Keyword(s):  
Perturbation Theory ◽  
Hydrogen Atom ◽  
Stark Effect ◽  
Symbolic Algorithms

scholarly journals Non-Hermitian Hamiltonian Treatment of Stark Effect in Quantum Mechanics

2020 ◽  
Vol 4 (6) ◽  
pp. 427-435
Author(s):  
Randal Hallford ◽  
Preet Sharma
Keyword(s):  
Perturbation Theory ◽  
Quantum Mechanics ◽  
Hydrogen Atom ◽  
Spherical Harmonics ◽  
Full Text ◽  
Stark Effect ◽  
Fundamental Level ◽  
Natural Processes

The Non-Hermitian aspect of Quantum Mechanics has been of great interest recently. There have been numerous studies on non-Hermitian Hamiltonians written for natural processes. Some studies have even expressed the hydrogen atom in a non-Hermitian basis. In this paper the principles of non-Hermitian quantum mechanics is applied to both the time independent perturbation theory and to the time dependant theory to calculate the Stark effect. The principles of spherical harmonics has also been used to describe the development in the non-Hermitian case. Finally, the non-Hermitian aspect has been introduced to the well known Stark effect in quantum mechanics to find a condition in which the Stark effect will still be true even if a non-Hermitian Hamiltonian is used. This study completes the understanding at a fundamental level to understand the well known Stark effect. Doi: 10.28991/esj-2020-01242 Full Text: PDF

scholarly journals The Stark effect with minimum length

2017 ◽  
Vol 32 (02n03) ◽  
pp. 1750010 ◽  
Author(s):  
H. L. C. Louzada ◽  
H. Belich
Keyword(s):  
Perturbation Theory ◽  
Energy Spectrum ◽  
Hydrogen Atom ◽  
Electric Field ◽  
Stark Effect ◽  
Heisenberg Algebra ◽  
Uniform Electric Field ◽  
Minimum Length

We will study the splitting in the energy spectrum of the hydrogen atom subjected to an uniform electric field (Stark effect) with the Heisenberg algebra deformed leading to the minimum length. We will use the perturbation theory for cases not degenerate (n[Formula: see text]=[Formula: see text]1) and degenerate (n[Formula: see text]=[Formula: see text]2), along with known results of corrections in these levels caused by the minimum length applied purely to the hydrogen atom, so that we may find and estimate the corrections of minimum length applied to the Stark effect.

scholarly journals NONCOMMUTATIVE CORRECTIONS TO THE MIC–KEPLER HAMILTONIAN

2005 ◽  
Vol 20 (04) ◽  
pp. 263-269 ◽  
Author(s):  
DENNIS KHETSELIUS
Keyword(s):  
Perturbation Theory ◽  
Hydrogen Atom ◽  
Stark Effect ◽  
Magnetic Monopole ◽  
Spherical Coordinates ◽  
Kepler System

Noncommutative corrections to the MIC–Kepler system (i.e. hydrogen atom in the presence of a magnetic monopole) are computed in Cartesian and spherical coordinates. In the framework of perturbation theory we were able to derive noncommutative corrections to the MIC–Kepler spectrum. We also found a nontrivial contribution to the linear Stark effect which did not exist in the standard hydrogen model.

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