Establishes uniqueness theorems for potential reconstruction in non-radial 2D/3D core-shell quantum fields from one ND-map measurement and proves nonuniqueness for varying potentials and shapes.
On uniqueness and nonuniqueness for potential reconstruction in quantum fields from one measurement
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abstract
This paper studies uniqueness and nonuniqueness for potential reconstruction from one boundary measurement in quantum fields, associated with the steady state Schr\"{o}dinger equation. A uniqueness theorem of the inverse problem is established. In the meanwhile, a nonuniqueness theorem is also given when different potential and shape are considered. Finally, Tikhonov regularization method is applied to solve the reconstruction problem, and some numerical examples are presented to confirm the theoretical results and the effectiveness of the proposed method.
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math.AP 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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On uniqueness and nonuniqueness for potential reconstruction in quantum fields from one measurement II. the non-radial case
Establishes uniqueness theorems for potential reconstruction in non-radial 2D/3D core-shell quantum fields from one ND-map measurement and proves nonuniqueness for varying potentials and shapes.