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Dispersive Estimates for Schrödinger Operators in Dimensions One and Three

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Abstract

We consider L1→L∞ estimates for the time evolution of Hamiltonians H=−Δ+V in dimensions d=1 and d=3 with bound We require decay of the potentials but no regularity. In d=1 the decay assumption is ∫(1+|x|)|V(x)|dx<∞, whereas in d=3 it is |V(x)|≤C(1+|x|)−3−.

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  1. Division of Astronomy, Mathematics and Physics, 253-37 Caltech, Pasadena, CA, 91125, USA

    M. Goldberg & W. Schlag

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  1. M. Goldberg
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  2. W. Schlag
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Correspondence to M. Goldberg.

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Communicated by B. Simon

Supported by the NSF grant DMS-0070538 and a Sloan fellowship.

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Goldberg, M., Schlag, W. Dispersive Estimates for Schrödinger Operators in Dimensions One and Three. Commun. Math. Phys. 251, 157–178 (2004). https://doi.org/10.1007/s00220-004-1140-5

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  • DOI: https://doi.org/10.1007/s00220-004-1140-5

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