Ground-State Energy Eigenvalues and Eigenfunctions for an Electron in an Electric-Dipole Field

1968 ◽  
Vol 174 (1) ◽  
pp. 81-89 ◽  
Author(s):  
J. E. Turner ◽  
V. E. Anderson ◽  
Kenneth Fox
Keyword(s):  
Ground State Energy ◽  
Electric Dipole ◽  
Ground State ◽  
State Energy ◽  
Dipole Field ◽  
Eigenvalues And Eigenfunctions ◽  
Energy Eigenvalues ◽  
Energy Eigenvalues And Eigenfunctions

Single-centre expansions for the hydrogen molecular ion. II

1962 ◽  
Vol 58 (1) ◽  
pp. 130-135 ◽  
Author(s):  
M. Cohen
Keyword(s):  
Ground State ◽  
State Energy ◽  
Internuclear Separation ◽  
Single Centre ◽  
Eigenvalues And Eigenfunctions ◽  
Exact Wave Function ◽  
Radial Functions ◽  
Energy Eigenvalues ◽  
Energy Eigenvalues And Eigenfunctions ◽  
Good Agreement

In an earlier paper (Cohen and Coulson(3), referred to hereafter as I), it was shown that satisfactory energy eigenvalues and eigenfunctions for various even σ-states of may be obtained using a single-centre expansion, provided that the radial functions are properly determined. In particular, the ground-state energy at the equilibrium internuclear separation of 2 a.u. was found to be within 0·25% of the exact value (Bates, Ledsham and Stewart (2)), and the eigenfunction reproduced all the characteristics of the exact wave-function. The method has now been extended to the odd σ-states, as well as to the two lowest π-states (2pπu, 3dπg), and the results are in good agreement with the calculations of Bates et al.

scholarly journals Analytical solution of energy eigen value, eigen function and angular wave function of Dirac equation with Rosen Morse plus Rosen Morse potential in terms of Romanovski polynomials for exact spin symmetry

2017 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Ihtiari Prasetyaningrum ◽  
C Cari ◽  
A Suparmi
Keyword(s):  
Dirac Equation ◽  
Morse Potential ◽  
State Energy ◽  
Spin Symmetry ◽  
Bound State ◽  
Bound State Energy ◽  
Eigenvalues And Eigenfunctions ◽  
Energy Eigenvalues ◽  
Eigen Value ◽  
Energy Eigenvalues And Eigenfunctions

<p class="Abstract">The energy eigenvalues and eigenfunctions of Dirac equation for Rosen Morse plus Rosen Morse potential are investigated numerically in terms of finite Romanovsky Polynomial. The bound state energy eigenvalues are given in a closed form and corresponding eigenfunctions are obtained in terms of Romanovski polynomials. The energi eigen value is solved by numerical method with Matlab 2011.</p>

Analytical solution of energy eigen value, eigen function and angular wave function of Dirac equation with Rosen Morse plus Rosen Morse potential in terms of Romanovski polynomials for exact spin symmetry

2017 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Ihtiari Prasetyaningrum ◽  
C Cari ◽  
A Suparmi
Keyword(s):  
Dirac Equation ◽  
Morse Potential ◽  
State Energy ◽  
Spin Symmetry ◽  
Bound State ◽  
Bound State Energy ◽  
Eigenvalues And Eigenfunctions ◽  
Energy Eigenvalues ◽  
Eigen Value ◽  
Energy Eigenvalues And Eigenfunctions

<p class="Abstract">The energy eigenvalues and eigenfunctions of Dirac equation for Rosen Morse plus Rosen Morse potential are investigated numerically in terms of finite Romanovsky Polynomial. The bound state energy eigenvalues are given in a closed form and corresponding eigenfunctions are obtained in terms of Romanovski polynomials. The energi eigen value is solved by numerical method with Matlab 2011.</p>

Analysis of the ground-state energy eigenvalues of fractal quantum potentials

2019 ◽  
Vol 94 (11) ◽  
pp. 115802
Author(s):  
Alireza Hashemi ◽  
Amir Hossein Darooneh
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Energy Eigenvalues

Relativistic ground-state energy eigenvalues of an electrondipole system

1971 ◽  
Vol 1 (2) ◽  
pp. 149-154 ◽  
Author(s):  
J. E. Turner ◽  
V. E. Anderson
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Energy Eigenvalues

The ground state energy of the ±J spin glass from the genetic algorithm

1994 ◽  
Vol 4 (9) ◽  
pp. 1281-1285 ◽  
Author(s):  
P. Sutton ◽  
D. L. Hunter ◽  
N. Jan
Keyword(s):  
Genetic Algorithm ◽  
Spin Glass ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy

POLARON IN A QUANTUM DOT UNDER AN ELECTRIC FIELD

2007 ◽  
Vol 21 (24) ◽  
pp. 1635-1642
Author(s):  
MIAN LIU ◽  
WENDONG MA ◽  
ZIJUN LI
Keyword(s):  
Quantum Dot ◽  
Electric Field ◽  
Field Intensity ◽  
Ground State Energy ◽  
Ground State ◽  
Electric Field Intensity ◽  
State Energy ◽  
Theoretical Study ◽  
The Moment ◽  
Transformation Methods

We conducted a theoretical study on the properties of a polaron with electron-LO phonon strong-coupling in a cylindrical quantum dot under an electric field using linear combination operator and unitary transformation methods. The changing relations between the ground state energy of the polaron in the quantum dot and the electric field intensity, restricted intensity, and cylindrical height were derived. The numerical results show that the polar of the quantum dot is enlarged with increasing restricted intensity and decreasing cylindrical height, and with cylindrical height at 0 ~ 5 nm , the polar of the quantum dot is strongest. The ground state energy decreases with increasing electric field intensity, and at the moment of just adding electric field, quantum polarization is strongest.

Effects of a scattering center on the ground-state energy of quantum-dot lithium

2017 ◽  
Vol 31 (07) ◽  
pp. 1750071
Author(s):  
Z. D. Vatansever ◽  
S. Sakiroglu ◽  
I. Sokmen
Keyword(s):  
Quantum Dot ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Electronic Charge ◽  
Strongly Correlated ◽  
Configuration Interaction Method ◽  
Charge Localization ◽  
Scattering Center ◽  
Spin Properties

In this paper, the effects of a repulsive scattering center on the ground-state energy and spin properties of a three-electron parabolic quantum dot are investigated theoretically by means of configuration interaction method. Phase transition from a weakly correlated regime to a strongly correlated regime is examined from several strengths and positions of Gaussian impurity. Numerical results reveal that the transition from spin-1/2 to spin-3/2 state depends strongly on the location of the impurity which accordingly states the controllability of the spin polarization. Moreover, broken circular symmetry results in more pronounced electronic charge localization.

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