On the Rapid Numerical Solution of the One-Dimensional Schrödinger Equation

1974 ◽  
Vol 52 (7) ◽  
pp. 664-665 ◽  
Author(s):  
John G. Wills
Keyword(s):  
Schrödinger Equation ◽  
Numerical Solution ◽  
Schrodinger Equation ◽  
New Method ◽  
One Dimensional ◽  
The One ◽  
Phase Amplitude

It is shown that the "new" method of rapid solution of the one-dimensional Schrödinger equation proposed by Newman and Thorson is equivalent to the well known phase–amplitude method.

Comment on Rapid Numerical Solution of the One Dimensional Schrodinger Equation

1974 ◽  
Vol 52 (24) ◽  
pp. 2509-2510 ◽  
Author(s):  
Walter R. Thorson
Keyword(s):  
Schrödinger Equation ◽  
Numerical Solution ◽  
Schrodinger Equation ◽  
Recent Article ◽  
One Dimensional ◽  
The One ◽  
Phase Amplitude

In a recent article Wills alleges that the method for rapid numerical solution of the one dimensional Schrodinger equation devised by Newman and Thorson "is equivalent to the well known phase-amplitude method". A critique of this opinion is given.

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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