Exact analytical solutions of the Schrödinger equation for a two dimensional purely sextic double-well potential

2018 ◽  
Vol 59 (3) ◽  
pp. 032101 ◽  
Author(s):  
Dai-Nam Le ◽  
Ngoc-Tram D. Hoang ◽  
Van-Hoang Le
Keyword(s):  
Schrödinger Equation ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Two Dimensional ◽  
Exact Analytical Solutions ◽  
Double Well Potential

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

A Hill-determinant approach to symmetric double-well potentials in two dimensions

1995 ◽  
Vol 73 (9-10) ◽  
pp. 632-637 ◽  
Author(s):  
M. R. M. Witwit ◽  
J. P. Killingbeck
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Dimensional Space ◽  
Energy Levels ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Degenerate Eigenvalues ◽  
Double Well Potential ◽  
Range Of Values

Energy levels of the Schrödinger equation for a double-well potential V(x,y;Z2,λ) = −Z2[x2 + y2] + λ[axxx4 + 2axyx2y2 + ayyy4] in two-dimensional space are calculated, using a Hill-determinant approach for several eigenstates and a range of values of λ and Z2. Special emphasis is placed on the larger values of Z2, for which the eigenvalues for different states have almost degenerate eigenvalues.

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.

scholarly journals Exact solutions of the radial Schrödinger equation for some physical potentials

Open Physics ◽  
2007 ◽  
Vol 5 (4) ◽  
Author(s):  
Sameer Ikhdair ◽  
Ramazan Sever
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Bound State ◽  
Two Dimensions ◽  
Exact Analytical Solutions ◽  
Radial Schrödinger Equation

AbstractBy using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrödinger equation for the pseudoharmonic and the Kratzer potentials in two dimensions. The bound-state solutions are easily calculated from this eigenfunction ansatz. The corresponding normalized wavefunctions are also obtained.

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