scholarly journals On the ambiguous treatment of the Schrödinger equation for the infinite potential well and an alternative via flat solutions: The one-dimensional case

2015 ◽  
Vol 17 (3) ◽  
pp. 333-351 ◽  
Author(s):  
Jesús Ildefonso Díaz
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Dimensional Case ◽  
Potential Well ◽  
One Dimensional ◽  
The One ◽  
Infinite Potential Well

scholarly journals Perturbation of the one-dimensional time-independent Schrödinger equation with a rectangular potential barrier

2020 ◽  
Vol 18 (1) ◽  
pp. 1413-1422
Author(s):  
Soon-Mo Jung ◽  
Ginkyu Choi
Keyword(s):  
Schrödinger Equation ◽  
Potential Barrier ◽  
Schrodinger Equation ◽  
Applied Mathematics ◽  
Finite Depth ◽  
Ulam Stability ◽  
Potential Well ◽  
One Dimensional ◽  
The One ◽  
Continuous Work

Abstract In Applied Mathematics Letters 74 (2017), 147–153, the Hyers-Ulam stability of the one-dimensional time-independent Schrödinger equation was investigated when the relevant system has a potential well of finite depth. As a continuous work, we prove in this paper a type of Hyers-Ulam stability of the one-dimensional time-independent Schrödinger equation with a rectangular potential barrier of {V}_{0} in height and 2c in width, where {V}_{0} is assumed to be greater than the energy E of the particle under consideration.

scholarly journals The Approximation Property of a One-Dimensional, Time Independent Schrödinger Equation with a Hyperbolic Potential Well

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1351
Author(s):  
Ginkyu Choi ◽  
Soon-Mo Jung
Keyword(s):  
Schrödinger Equation ◽  
Potential Function ◽  
Schrodinger Equation ◽  
Approximation Property ◽  
Ulam Stability ◽  
Potential Well ◽  
One Dimensional ◽  
Parabolic Potential ◽  
Hyperbolic Potential ◽  
The One

A type of Hyers–Ulam stability of the one-dimensional, time independent Schrödinger equation was recently investigated; the relevant system had a parabolic potential wall. As a continuation, we proved a type of Hyers–Ulam stability of the time independent Schrödinger equation under the action of a specific hyperbolic potential well. One of the advantages of this paper is that it proves a type of Hyers–Ulam stability of the Schrödinger equation under the condition that the potential function has singularities.

A TWELFTH-ORDER FOUR-STEP FORMULA FOR THE NUMERICAL INTEGRATION OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION

2003 ◽  
Vol 14 (08) ◽  
pp. 1087-1105 ◽  
Author(s):  
ZHONGCHENG WANG ◽  
YONGMING DAI
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Numerical Test ◽  
New Method ◽  
Step Method ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Order Four

A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.

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