Accurately solving the electronic Schrödinger equation of atoms and molecules using explicitly correlated (r12-)MR-CI. II. Ground-state energies of first-row atoms and positive atomic ions

1998 ◽  
Vol 109 (22) ◽  
pp. 9795-9801 ◽  
Author(s):  
Robert J. Gdanitz
Keyword(s):  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Atomic Ions ◽  
Atoms And Molecules ◽  
Explicitly Correlated ◽  
Ground State Energies

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.

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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