A high-order accuracy method for numerical solving of the time-dependent Schrödinger equation (Q1961779)
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scientific article; zbMATH DE number 1394619
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A high-order accuracy method for numerical solving of the time-dependent Schrödinger equation |
scientific article; zbMATH DE number 1394619 |
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A high-order accuracy method for numerical solving of the time-dependent Schrödinger equation (English)
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20 July 2000
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The paper presents the implicit difference \(O(\tau^{2m})\)-schemes in terms of the Magnus expansion for the evolution operator of the time-dependent Schrödinger equation and its further factorization with the help of diagonal Padé approximations. These schemes can be viewed as generalization of the well-known Crank-Nicolson algorithm. The efficiency of the method is illustrated by numerical experiments for the oscillator with time-dependent frequency.
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Schrödinger equation
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Magnus expansion
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Padé approximation
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Crank-Nicolson algorithm
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implicit difference schemes
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numerical experiments
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oscillator
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0.9493961
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0.93669033
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0.9276181
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0.9223562
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0.9212889
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