scholarly journals Error estimates of Crank–Nicolson Galerkin method for the time-dependent Maxwell–Schrödinger equations under the Lorentz gauge

2017 ◽  
Vol 38 (4) ◽  
pp. 2074-2104 ◽  
Author(s):  
Chupeng Ma ◽  
Liqun Cao ◽  
Yanping Lin
Keyword(s):  
Galerkin Method ◽  
Error Estimates ◽  
Time Dependent ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Lorentz Gauge ◽  
Crank Nicolson

Higher order exponential split operator method for solving time-dependent Schrödinger equations

1992 ◽  
Vol 70 (2) ◽  
pp. 555-559 ◽  
Author(s):  
André D. Bandrauk ◽  
Hai Shen
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Operator Method ◽  
Computation Time ◽  
Time Dependent ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Exponential Form ◽  
Operator Solution ◽  
Split Operator

A new method of splitting exponential operators is proposed for the exponential form of the operator solution to the time-dependent Schrödinger equation. The method is shown to hold for any desired accuracy in the time increment. A comparison of different algorithms is made as a function of accuracy and computation time. Keywords: splitting operator, Fast Fourier Transform (FFT), Schrödinger equations.

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