Efficient finite difference solutions to the time-dependent Schrödinger equation (Q676367)
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scientific article; zbMATH DE number 992139
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Efficient finite difference solutions to the time-dependent Schrödinger equation |
scientific article; zbMATH DE number 992139 |
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Efficient finite difference solutions to the time-dependent Schrödinger equation (English)
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14 May 1998
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For solving the initial value and time-dependent problem for the Schrödinger equation an expansion of the evolution operator in terms of unitary anti-Hermitian operators is used. The one-dimensional Laplacian is represented by the standard finite difference approximation of second order and the corresponding exponential is calculated exactly by means of Bessel functions. The proposed algorithms are generalized to two spatial dimensions.
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Schrödinger equation
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evolution operator
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finite difference
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Bessel functions
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algorithms
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