On multidimensional inverse scattering under the Stark effect

We study one of multidimensional inverse scattering problems for quantum systems in a constant electric field, by utilization of the Enss-Weder time-dependent method. The main purpose of this paper is to propose some methods of sharpening key estimates in the analysis, which are much simpler than those in the previous works. Our methods give an appropriate class of short-range potentials which can be determined uniquely by scattering operators, that seems natural in terms of direct scattering problems.

[1]  Atsuhide Ishida.  Inverse scattering in the Stark effect , 2018, Inverse Problems.

[2]  Atsuhide Ishida,et al.  On multidimensional inverse scattering in time-dependent electric fields , 2013 .

[3]  T. Adachi,et al.  On multidimensional inverse scattering in an external electric field asymptotically zero in time , 2011 .

[4]  R. Weder,et al.  High-velocity estimates and inverse scattering for quantum N-body systems with Stark effect , 2011, 1103.6182.

[5]  T. Adachi,et al.  On multidimensional inverse scattering for Stark Hamiltonians , 2007 .

[6]  R. Weder.  Multidimensional inverse scattering in an electric field , 1996 .

[7]  R. Weder,et al.  The geometrical approach to multidimensional inverse scattering , 1995 .

[8]  D. A. W. White.  Modified wave operators and Stark Hamiltonians , 1992 .

[9]  V. Enss.  Propagation properties of quantum scattering states , 1983 .

[10]  K. Yajima.  Spectral and scattering theory for Schrodinger operators with Stark-effect, II , 1979 .

[11]  V. Enss.  Asymptotic completeness for quantum mechanical potential scattering , 1978 .

[12]  J. Zorbas.  Scattering theory for Stark Hamiltonians involving long‐range potentials , 1978 .

[13]  I. Herbst,et al.  Spectral and scattering theory of Schrödinger operators related to the stark effect , 1977 .

[14]  I. Herbst.  Unitary equivalence of stark Hamiltonians , 1977 .

[15]  F. Nicoleau.  Inverse scattering for Stark Hamiltonians with short‐range potentials , 2003 .

[16]  H. Tamura,et al.  Asymptotic completeness for long-range many-particle systems with Stark effect. II , 1995 .

[17]  G. M. Graf.  A remark on long-range Stark scattering , 1991 .

[18]  A. Jensen,et al.  On the long range scattering for Stark Hamiltonians. , 1991 .

[19]  S. Helgason.  Groups and geometric analysis , 1984 .

[20]  Barry Simon,et al.  Methods of modern mathematical physics. III. Scattering theory , 1979 .