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.

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.

HYPERSPHERICAL APPROACH TO STUDY THE SCHRÖDINGER EQUATION FOR AN N-PARTICLE SYSTEM

2009 ◽  
Vol 18 (07) ◽  
pp. 1497-1502
Author(s):  
H. HASSANABADI ◽  
A. A. RAJABI ◽  
M. M. SHOJAEI
Keyword(s):  
Analytical Solution ◽  
Schrödinger Equation ◽  
Excited States ◽  
Ground State ◽  
Schrodinger Equation ◽  
Particle System ◽  
Exact Analytical Solution ◽  
Hyperspherical Approach

In the present work we give an exact analytical solution of the Schrödinger equation for an N-particle system by using the hyperspherical approach, in the presence of the hypercentral potential of form V(R) = a1R2+b1R-4+c1R-6 for both the ground state and the excited states.

Exact analytical solutions of higher-order nonlinear Schrödinger equation

Optik ◽  
2017 ◽  
Vol 131 ◽  
pp. 438-445 ◽  
Author(s):  
Hongcheng Wang ◽  
Jianchu Liang ◽  
Guihua Chen ◽  
Ling Zhou ◽  
Dongxiong Ling ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Exact Analytical Solutions ◽  
Nonlinear Schrödinger

scholarly journals Algebraic approach to non-separable two-dimensional Schrödinger equation: Ground states for polynomial and Morse-like potentials

Open Physics ◽  
2014 ◽  
Vol 12 (10) ◽  
Author(s):  
Vladimír Tichý ◽  
Lubomír Skála ◽  
René Hudec
Keyword(s):  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Ground States ◽  
Algebraic Approach ◽  
Algebraic Method ◽  
Analytic Solutions ◽  
Wave Functions ◽  
Two Dimensional ◽  
One Dimensional

AbstractThis paper presents a direct algebraic method of searching for analytic solutions of the two-dimensional time-independent Schrödinger equation that is impossible to separate into two one-dimensional ones. As examples, two-dimensional polynomial and Morse-like potentials are discussed. Analytic formulas for the ground state wave functions and the corresponding energies are presented. These results cannot be obtained by another known method.

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