4,462 research outputs found
New Variational Principles in Classical and Semiclassical Mechanics
We demonstrate that reciprocal Maupertuis' Principle is the classical limit
of Schr\"{o}dinger's Variational Principle in Quantum Mechanics.Comment: To appear in the Michael Marinov Memorial Volume, "Multiple facets of
quantization and supersymmetry", edited by M. Olshanetsky and A. Vainshtein
(World Scientific). We corrected TEX style of the paper so that the names of
both authors can be seen in PS file no
New global stability estimates for the Gel'fand-Calderon inverse problem
We prove new global stability estimates for the Gel'fand-Calderon inverse
problem in 3D. For sufficiently regular potentials this result of the present
work is a principal improvement of the result of [G. Alessandrini, Stable
determination of conductivity by boundary measurements, Appl. Anal. 27 (1988),
153-172]
The Moutard transformation and two-dimensional multi-point delta-type potentials
In the framework of the Moutard transformation formalism we find multi-point
delta-type potentials of two-dimensional Schrodinger operators and their
isospectral deformations on the zero energy level. In particular, these
potentials are "reflectionless" in the sense of the Faddeev generalized
"scattering" data.Comment: 4 page
Weighted Radon transforms for which the Chang approximate inversion formula is precise
We describe all weighted Radon transforms on the plane for which the Chang
approximate inversion formula is precise. Some subsequent results, including
the Cormack type inversion for these transforms, are also given
Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential
For the Schrodinger equation at fixed energy with a potential supported in a
bounded domain we give formulas and equations for finding scattering data from
the Dirichlet-to-Neumann map with nonzero background potential. For the case of
zero background potential these results were obtained in [R.G.Novikov,
Multidimensional inverse spectral problem for the equation
-\Delta\psi+(v(x)-Eu(x))\psi=0, Funkt. Anal. i Ego Prilozhen 22(4), pp.11-22,
(1988)]
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