Abstract
We describe smoothing effects and dispersion of singularities for the Schrödinger evolution group in the weighted Sobolev spaces. Under a fairly general assumption on the potential, it is shown that all singularities in the wavefunction vanish instantly whenever the initial state has sufficient decay. We measure the regularity gained by the wavefunction by the decay property of the initial state. No assumptions on the regularity of the initial state are imposed throughout the paper.
| Original language | English |
|---|---|
| Pages (from-to) | 165-186 |
| Number of pages | 22 |
| Journal | Archive for Rational Mechanics and Analysis |
| Volume | 110 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1990 May |
| Externally published | Yes |
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ASJC Scopus subject areas
- Mathematics (miscellaneous)
- Mathematics(all)
- Mechanics of Materials
- Computational Mechanics
Cite this
Smoothing effects and dispersion of singularities for the Schrödinger evolution group. / Ozawa, Tohru.
In: Archive for Rational Mechanics and Analysis, Vol. 110, No. 2, 05.1990, p. 165-186.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Smoothing effects and dispersion of singularities for the Schrödinger evolution group
AU - Ozawa, Tohru
PY - 1990/5
Y1 - 1990/5
N2 - We describe smoothing effects and dispersion of singularities for the Schrödinger evolution group in the weighted Sobolev spaces. Under a fairly general assumption on the potential, it is shown that all singularities in the wavefunction vanish instantly whenever the initial state has sufficient decay. We measure the regularity gained by the wavefunction by the decay property of the initial state. No assumptions on the regularity of the initial state are imposed throughout the paper.
AB - We describe smoothing effects and dispersion of singularities for the Schrödinger evolution group in the weighted Sobolev spaces. Under a fairly general assumption on the potential, it is shown that all singularities in the wavefunction vanish instantly whenever the initial state has sufficient decay. We measure the regularity gained by the wavefunction by the decay property of the initial state. No assumptions on the regularity of the initial state are imposed throughout the paper.
UR - http://www.scopus.com/inward/record.url?scp=0039222903&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0039222903&partnerID=8YFLogxK
U2 - 10.1007/BF00873497
DO - 10.1007/BF00873497
M3 - Article
AN - SCOPUS:0039222903
VL - 110
SP - 165
EP - 186
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
SN - 0003-9527
IS - 2
ER -