The first solution of a long standing problem: Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrödinger equation
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Abstract
A long standing problem is completely solved here for the first time. This problem was posed by K. Chadan and P. C. Sabatier in their classical book “Inverse Problems in Quantum Scattering Theory”, Springer, New York, 1977. The inverse scattering problem of the reconstruction of the unknown potential with a compact support in the three-dimensional Schrödinger equation is considered. Only the modulus of the scattering complex-valued wave field is known, whereas the phase is unknown. It is shown that the unknown potential can be reconstructed via the inverse Radon transform. This solution has potential applications in imaging of nanostructures.
Funding source: US Army Research Laboratory and US Army Research Office
Award Identifier / Grant number: #W911NF-15-1-0233
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 14-01-00208
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- The interior transmission eigenvalue problem for a spherically-symmetric domain with anisotropic medium and a cavity
- Ill-conditioning versus ill-posedness for the boundary controllability of the heat equation
- Parameters identification in the mathematical model of immune competition cells
- Inverse source problems for time-fractional mixed parabolic-hyperbolic-type equations
- Model parameter estimation of linear time-invariant systems from combined data of forced and initial condition responses
- An inverse problem for the Vlasov–Poisson system
- An inexact Newton regularization in Banach spaces based on the nonstationary iterated Tikhonov method
- Multilevel preconditioning for sparse optimization of functionals with nonconvex fidelity terms
- The first solution of a long standing problem: Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrödinger equation
Articles in the same Issue
- Frontmatter
- The interior transmission eigenvalue problem for a spherically-symmetric domain with anisotropic medium and a cavity
- Ill-conditioning versus ill-posedness for the boundary controllability of the heat equation
- Parameters identification in the mathematical model of immune competition cells
- Inverse source problems for time-fractional mixed parabolic-hyperbolic-type equations
- Model parameter estimation of linear time-invariant systems from combined data of forced and initial condition responses
- An inverse problem for the Vlasov–Poisson system
- An inexact Newton regularization in Banach spaces based on the nonstationary iterated Tikhonov method
- Multilevel preconditioning for sparse optimization of functionals with nonconvex fidelity terms
- The first solution of a long standing problem: Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrödinger equation
