Simple exact solution of the one-dimensional Schrödinger equation with continuous plusδ-function potentials of arbitrary position and strength

1980 ◽  
Vol 22 (2) ◽  
pp. 765-766 ◽  
Author(s):  
J. Ronald Farias
Keyword(s):  
Exact Solution ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
One Dimensional ◽  
Arbitrary Position ◽  
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.

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