Abstract
We discuss algorithms for the solution of the Schrödinger time-dependent equation, based on orthogonal polynomial decomposition of the exponential function. After reviewing the classical Chebyshev series approach and its iterated version, we show their inefficiency when applied to operators with singular continuous spectral measures. We then introduce new decompositions based on the spectral measure of the problem under consideration, which are especially suited to deal with this case. A fast version of these algorithms is also developed and shown to achieve the theoretical maximum performance.
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© 1999 Springer Basel AG
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Mantica, G. (1999). Fourier Transforms of Orthogonal Polynomials of Singular Continuous Spectral Measures. In: Gautschi, W., Opfer, G., Golub, G.H. (eds) Applications and Computation of Orthogonal Polynomials. International Series of Numerical Mathematics, vol 131. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8685-7_11
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DOI: https://doi.org/10.1007/978-3-0348-8685-7_11
Publisher Name: Birkhäuser, Basel
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