Variational calculation of ground-state energy of iron atoms and condensed matter in strong magnetic fields

1977 ◽  
Vol 215 ◽  
pp. 291 ◽  
Author(s):  
E. G. Flowers ◽  
M. A. Ruderman ◽  
J.-F. Lee ◽  
P. G. Sutherland ◽  
W. Hillebrandt ◽  
...  
Keyword(s):  
Magnetic Fields ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Condensed Matter ◽  
Variational Calculation ◽  
Strong Magnetic Fields

Hydrogen and helium atoms in strong magnetic fields

1985 ◽  
Vol 63 (8) ◽  
pp. 1022-1028 ◽  
Author(s):  
T. O. Hansen ◽  
E. Østgaard
Keyword(s):  
Hydrogen Atom ◽  
Magnetic Fields ◽  
Ground State ◽  
State Energy ◽  
Variational Calculation ◽  
Strong Magnetic Fields ◽  
Ionization Energies ◽  
One Dimensional ◽  
Helium Atoms ◽  
Ground State Energies

The behaviour of atoms in strong magnetic fields of the order of 106–1012 G is investigated, and ground-state energies of hydrogenlike and heliumlike atoms are calculated and compared with earlier results. For the hydrogen atom, we make a variational calculation for so-called hydrogenlike states, where we assume the solution in the direction of the field corresponds to the solution of a one-dimensional Schrödinger equation with a truncated Coulomb potential. For the helium atoms we also try a variational approach where the trial wave functions are products of single-particle "orbitals," which are mainly magnetic in their spatial form.Ground-state energies and ionization energies are tabulated for field strengths ranging from 106 to 1012 G. At 1012 G, for instance, the binding energy of a hydrogen atom is changed from −13.6 eV to approximately −150 eV, which is in reasonable agreement with other calculations. The corresponding result for the ground-state energy of a helium atom is a change from −78 eV to approximately −730 eV, also in fair agreement with other calculations. Ionization energies for the outer electron are found to be approximately 50 eV for H− atoms and 350 eV for He atoms in a magnetic field of 1012 G.

Rapidly Converging Bounds for the Ground-State Energy of Hydrogenic Atoms in Superstrong Magnetic Fields

1988 ◽  
Vol 60 (4) ◽  
pp. 253-256 ◽  
Author(s):  
Carlos R. Handy ◽  
Daniel Bessis ◽  
Gabriel Sigismondi ◽  
Thomas D. Morley
Keyword(s):  
Magnetic Fields ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy

Variational calculation on ground-state energy of bound polarons in parabolic quantum wires

2001 ◽  
Vol 10 (5) ◽  
pp. 437-442 ◽  
Author(s):  
Wang Zhuang-bing ◽  
Wu Fu-li, Chen Qing-hu ◽  
Jiao Zheng-kuan
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Quantum Wires ◽  
Variational Calculation

Ground State Energy of Polaron Bound in a Coulomb Potential

1974 ◽  
Vol 52 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Mitsuru Matsuura
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
Present Method ◽  
State Energy ◽  
Variational Calculation ◽  
Effective Potentials ◽  
Important Region ◽  
Electron Phonon Coupling ◽  
Wide Range ◽  
Path Integral Method

The path integral method is used to obtain an expression, involving a sum over the complete set of solutions for the effective trial Hamiltonian, for the ground state energy of the bound polaron. The numerical calculations of this expression are performed for the hydrogenic and harmonic oscillator effective potentials. The present method together with several previous theories and their numerical results are discussed over a wide range of the electron–phonon coupling constant α and the electron–massive hole coupling β. It is shown that, for the experimentally important region, the present method with the hydrogenic potential yields the lowest energy—slightly lower than obtained by the Larsen's variational calculation.

INFLUENCE OF BOTH ELECTRIC AND MAGNETIC FIELDS ON THE POLARON IN A CYLINDRICAL QUANTUM DOT

2004 ◽  
Vol 18 (20n21) ◽  
pp. 2887-2899 ◽  
Author(s):  
RUI-QIANG WANG ◽  
HONG-JING XIE ◽  
YOU-BIN YU
Keyword(s):  
Magnetic Fields ◽  
Quantum Dot ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Side Surface ◽  
Energy Shift ◽  
Longitudinal Optical ◽  
Electric And Magnetic Fields ◽  
The Magnetic Field

The polaronic correction to the ground-state energy of the electron confined in a cylindrical quantum dot (QD) subject to electric and magnetic fields along the growth axis has been investigated. Using a combinative approach of perturbative theory and variational wavefunction, calculations are performed for an infinitely deep confinement potential outside the QD within the effective mass and adiabatic approximation. We have treated the system by taking into consideration the interaction of the electron with the confined longitudinal optical (LO) phonons as well as the side surface (SSO) and the top surface (TSO) optical phonons.1,2 The ground-state energy shift is obtained as a function of the cylindrical radius and the strength of electric and magnetic fields. The results show that the magnetic field heavily enhances the three types of phonon mode contribution to the correction of the electron ground-state energy while the electric field only improves the contribution of surface phonons (SSO and TSO) but decreases the contribution of LO phonons.

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