Exact solution of the one-dimensional time-dependent Schrödinger equation with a rectangular well/barrier potential and its applications

2013 ◽  
Vol 177 (3) ◽  
pp. 1706-1721 ◽  
Author(s):  
V. F. Los ◽  
N. V. Los
Keyword(s):  
Exact Solution ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
One Dimensional ◽  
Barrier Potential ◽  
The One

A new method of exact solution generation for the one-dimensional Schrödinger equation

1990 ◽  
Vol 147 (7) ◽  
pp. 348-350 ◽  
Author(s):  
V.G Bagrov ◽  
A.V Shapovalov ◽  
I.V Shirokov
Keyword(s):  
Exact Solution ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
New Method ◽  
One Dimensional ◽  
Solution Generation ◽  
The One

Analytic time-dependent solutions of the one-dimensional Schrödinger equation

2014 ◽  
Vol 82 (10) ◽  
pp. 955-961 ◽  
Author(s):  
Wytse van Dijk ◽  
F. Masafumi Toyama ◽  
Sjirk Jan Prins ◽  
Kyle Spyksma
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
One Dimensional ◽  
The One

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.

Sign in / Sign up

Export Citation Format

Share Document