Note on the wave functions used for point-ion-lattice calculations of F-centres

1966 ◽  
Vol 19 (12) ◽  
pp. 2193
Author(s):  
CK Coogan ◽  
HG Hecht
Keyword(s):  
Ground State ◽  
Hyperfine Coupling ◽  
Spherical Wave ◽  
Alkali Halides ◽  
Higher Order ◽  
Wave Functions ◽  
Crystal Symmetry ◽  
Basis Set ◽  
Slater Type ◽  
Ground State Energies

Slater type ns wave functions, differing from the spherically symmetrical wave functions used by Gourary and Adrian, have been tried as a basis set for calculating wave functions of electrons in F-centres in alkali halides. Combinations of 1s, 2s, and 3s Slater functions still yielded ground state energies slightly higher than that calculated by Gourary and Adrian. It is concluded both that the GA wave functions were very well chosen and that more significant changes, particularly in the calculated hyperfine coupling, would come from adding terms of higher-order harmonics, compatible with the crystal symmetry, to the spherical wave functions.

TWO-ELECTRON SYSTEM IN THE FIELD OF GENERALIZED SCREENED POTENTIAL

2011 ◽  
Vol 25 (19) ◽  
pp. 1619-1629 ◽  
Author(s):  
ARIJIT GHOSHAL ◽  
Y. K. HO
Keyword(s):  
Wave Function ◽  
Ground State ◽  
Electron System ◽  
Wave Functions ◽  
Expectation Values ◽  
Screening Parameter ◽  
System Ground State ◽  
Highly Correlated ◽  
First Time ◽  
Ground State Energies

Ground states of a two-electron system in generalized screened potential (GSP) with screening parameter λ: [Formula: see text] where ∊ is a constant, have been investigated. Employing highly correlated and extensive wave functions in Ritz's variational principle, we have been able to determine accurate ground state energies and wave functions of a two-electron system for different values of the screening parameter λ and the constant ∊. Convergence of the ground state energies with the increase of the number of terms in the wave function are shown. We also report various geometrical expectation values associated with the system, ground state energies of the corresponding one-electron system and the ionization potentials of the system. Such a calculation for the ground state of a two-electron system in GSP is carried out for first time in the literature.

Molecular orbitals in momentum space

1965 ◽  
Vol 286 (1406) ◽  
pp. 376-389 ◽  
Keyword(s):  
Momentum Space ◽  
Wave Functions ◽  
Basis Set ◽  
Equilibrium Distance ◽  
Numerical Work ◽  
Algebraic Expressions ◽  
Unitary Transformations ◽  
The Matrix ◽  
Internuclear Distances ◽  
Ground State Energies

The troublesome problem of developing cusps in ordinary molecular wave functions can be avoided by working with momentum-space wavefunctions for these have no cusps. The need for continuum wavefunctions can be eliminated if one works with a hydrogenic basis set in Fock’s projective momentmn space. This basis set is the set of R 4 spherical harmonics and as a consequence one may obtain, solely by the ordinary angular momentum calculus, algebraic expressions for all the integrals required in the solution of the momentum space Schrödinger equation. A number of these integrals and a number of R 4 transformation coefficients are tabulated. The method is then applied to several simple united-atom and l.c.a.o. wavefunctions for H + 2 and ground state energies and corrected wavefunctions are obtained. It is found in this numerical work that the method is most appropriate at internuclear distances somewhat less than the equilibrium distance. In Fock’s representation both l.c.a.o. and unitedatom approximations become exact as the internuclear distance approaches zero. The united-atom expansion can be viewed as an eigenvalue equation for the root-mean-square momentum, p 0 = √( — 2 E ). In the molecule, the matrix operator corresponding to p 0 is related to the operator for the united-atom by a sum of unitary transformations, one for each nucleus in the molecule.

Theoretical Calculations of Relative Intensities in Hyperfine Diatomic Transitions

1974 ◽  
Vol 52 (4) ◽  
pp. 361-368 ◽  
Author(s):  
J. L. Féménias ◽  
C. Athénour ◽  
R. Stringat
Keyword(s):  
Dipole Moment ◽  
Intensity Distribution ◽  
Ground State ◽  
Hyperfine Coupling ◽  
Theoretical Calculations ◽  
Electronic States ◽  
Wave Functions ◽  
Optical Transitions ◽  
Matrix Elements ◽  
Coupling Case

A method of calculating molecular wave functions in complex 'hyperfine' coupling cases is presented. It enables us to express (bβJ) and (bβS) wave functions in terms of more simple (aβ) functions, and to connect their parities and symmetry characters to those of 'classical' (b) wave functions. With the help of these expansions of (bβJ) and (bβS) wave functions, we have carried out the calculation of the reduced matrix elements of electric dipole moment M in order to study the intensity distribution in optical transitions between excited diatomic electronic states belonging to the (aβ), (intermediate aβ–bβJ), and (bβJ) coupling case, and a ground state belonging to the (bβS) coupling case. First comparisons with experimental results in the ScO molecule are made, and these enable us to give theoretical confirmation to some previous assumptions.

Analytic energies and wave functions of the two-dimensional Schrödinger equation: ground state of two-dimensional quartic potential and classification of solutions

2012 ◽  
Vol 90 (6) ◽  
pp. 503-513 ◽  
Author(s):  
Vladimír Tichý ◽  
Aleš Antonín Kuběna ◽  
Lubomír Skála
Keyword(s):  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Analytic Solutions ◽  
Wave Functions ◽  
Two Dimensional ◽  
Quartic Potential ◽  
Ground State Energies ◽  
Fourth Order Polynomial

New analytic solutions of the two-dimensional Schrödinger equation with a two-dimensional fourth-order polynomial (i.e., quartic) potential are derived and discussed. The solutions represent the ground state energies and the corresponding wave functions. In general, the obtained results cannot be reduced to two one-dimensional cases.

VARIATIONAL COMPUTATIONS FOR EXCITONS IN QUANTUM DOTS: A QUANTUM MONTE CARLO STUDY

2011 ◽  
Vol 25 (01) ◽  
pp. 119-130
Author(s):  
A. YILDIZ ◽  
S. ŞAKİROĞLU ◽  
Ü. DOĞAN ◽  
K. AKGÜNGÖR ◽  
H. EPİK ◽  
...  
Keyword(s):  
Quantum Dots ◽  
Monte Carlo ◽  
Ground State ◽  
Quantum Monte Carlo ◽  
Three Dimensional ◽  
Monte Carlo Study ◽  
Wave Functions ◽  
Monte Carlo Techniques ◽  
Oscillator Basis ◽  
Ground State Energies

A study of variational wave functions for calculation of the ground-state energies of excitons confined in a two-dimensional (2D) disc-like and three-dimensional (3D) spherical parabolic GaAs quantum dots (QDs) is presented. We have used four variational trial wave functions constructed as the harmonic-oscillator basis multiplied by different correlation functions. The proposed correlation function formed by including linear expansion in terms of Hylleraas-like coordinates to the Jastrow factor is able to capture nearly exactly the ground-state energies of 3D excitons, and it properly account for the results of 2D excitons. Quantum Monte Carlo techniques combined with the proposed wave function are a powerful tool for studying excitons in parabolic QDs.

Analytical Solutions of the Schrödinger Equation. Ground State Energies and Wave Functions

1998 ◽  
Vol 63 (8) ◽  
pp. 1161-1176 ◽  
Author(s):  
Jan Dvořák ◽  
Lubomír Skála
Keyword(s):  
Schrödinger Equation ◽  
Excited States ◽  
Analytical Solutions ◽  
Ground State ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Exact Analytical Solutions ◽  
Ground State Energies ◽  
Solvable Problems

It is shown that there are two generalizations of some well-known analytically solvable problems leading to exact analytical solutions of the Schrödinger equation for the ground state and a few low lying excited states. In this paper, the ground state energies and wave functions are discussed.

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