Quantum Chaos and Statistical Properties of Energy Levels: Numerical Study of the Hydrogen Atom in a Magnetic Field

1986 ◽  
Vol 57 (16) ◽  
pp. 2006-2009 ◽  
Author(s):  
D. Delande ◽  
J. C. Gay
Keyword(s):  
Magnetic Field ◽  
Hydrogen Atom ◽  
Quantum Chaos ◽  
Numerical Study ◽  
Energy Levels ◽  
Statistical Properties

Quantum chaos and statistical properties of energy levels for atom in parallel electric and magnetic fields

2015 ◽  
Vol 29 (35n36) ◽  
pp. 1550248
Author(s):  
Hai-Feng Yang ◽  
Yong-Gang Tan ◽  
Zhong-Li Liu ◽  
Hong-Zhi Fu
Keyword(s):  
Magnetic Fields ◽  
Quantum Chaos ◽  
Chaotic Dynamics ◽  
Nearest Neighbor ◽  
Energy Levels ◽  
Statistical Properties ◽  
The Core ◽  
Ideal System ◽  
Electric And Magnetic Fields ◽  
Diagonalization Method

In this paper, the statistical properties of energy levels are studied numerically for atom in parallel electric and magnetic fields, which is an ideal system to examine the contributions of external fields and ionic core to quantum chaos. The Stark maps of diamagnetic spectra and nearest neighbor spacing (NNS) distributions are obtained by diagonalization method incorporating core effect. We identify obvious level anti-crossing and large value of [Formula: see text] for barium, indicating that core effect has predominant contribution to chaotic dynamics in barium. To study the core effect in detail, we sweep the quantum defect artificially and find that larger core effect will undoubtedly induce stronger chaotic dynamics.

scholarly journals NEW TREATMENT OF THE NONCOMMUTATIVE DIRAC EQUATION WITH A COULOMB POTENTIAL

2012 ◽  
Vol 27 (19) ◽  
pp. 1250100 ◽  
Author(s):  
LAMINE KHODJA ◽  
SLIMANE ZAIM
Keyword(s):  
Magnetic Field ◽  
Field Equation ◽  
Hydrogen Atom ◽  
Dirac Equation ◽  
Hyperfine Structure ◽  
Coulomb Potential ◽  
Energy Levels ◽  
Nonrelativistic Limit ◽  
New Treatment

Using the approach of the modified Euler–Lagrange field equation together with the corresponding Seiberg–Witten maps of the dynamical fields, a noncommutative Dirac equation with a Coulomb potential is derived. We then find the noncommutative modification to the energy levels and the possible new transitions. In the nonrelativistic limit a general form of the Hamiltonian of the hydrogen atom is obtained, and we show that the noncommutativity plays the role of spin and magnetic field which gives the hyperfine structure.

Energy levels of a hydrogen atom in a magnetic field

1994 ◽  
Vol 50 (1) ◽  
pp. 861-862 ◽  
Author(s):  
J. X. Zang ◽  
M. L. Rustgi
Keyword(s):  
Magnetic Field ◽  
Hydrogen Atom ◽  
Energy Levels

Summation of the perturbation series for the energy levels of a hydrogen atom in a magnetic field

1983 ◽  
Vol 102 (4) ◽  
pp. 344-353 ◽  
Author(s):  
Gustavo A. Arteca ◽  
Francisco M. Fernandez ◽  
Eduardo A. Castro
Keyword(s):  
Magnetic Field ◽  
Hydrogen Atom ◽  
Energy Levels ◽  
Perturbation Series

scholarly journals CHAOS, FRACTALS AND QUANTUM POINCARÉ RECURRENCES IN DIAMAGNETIC KEPLER PROBLEM

2007 ◽  
Vol 21 (02n03) ◽  
pp. 79-96 ◽  
Author(s):  
A. UGULAVA ◽  
L. CHOTORLISHVILI ◽  
T. KERESELIDZE ◽  
V. SKRINNIKOV
Keyword(s):  
Magnetic Field ◽  
Hilbert Space ◽  
Hydrogen Atom ◽  
Strong Magnetic Field ◽  
Quantum Chaos ◽  
Kepler Problem ◽  
Quantum Mechanical ◽  
Mechanical State ◽  
Classical Chaos ◽  
Good Agreement

The statistics of quantum Poincaré recurrences in Hilbert space for diamagnetic hydrogen atom in strong magnetic field has been investigated. It has been shown that quantities characterizing classical chaos are in good agreement with the ones that are used to describe quantum chaos. The equality of classical and quantum Poincaré recurrences has been shown. It has been proved that one of the signs of the emergence of quantum chaos is the irreversible transition from a pure quantum mechanical state to a mixed one.

scholarly journals Regularity and Chaos in the Hydrogen Atom Highly Excited with a Strong Magnetic Field

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
M. Amdouni ◽  
H. Eleuch
Keyword(s):  
Magnetic Field ◽  
Hydrogen Atom ◽  
Strong Magnetic Field ◽  
Energy Levels ◽  
Energy Spectra ◽  
Recoil Energy ◽  
Continuous Energy ◽  
Relativistic Corrections ◽  
Nucleus Mass

The effects of the relativistic corrections on the energy spectra are analyzed. Effective simulations based on manipulations of operators in the Sturmian basis are developed. Discrete and continuous energy spectra of a hydrogen atom with realistic nucleus mass in a strong magnetic field are computed. The transition from regularity to chaos in diamagnetic problem with the effect of the nucleus recoil energy is explored. Anticrossing of energy levels is observed for strong magnetic field.

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