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- W1694173860 abstract "Consider the Schrodinger operator $-nabla^2+q$ $ $q$, $q=q(x), x in mathbf{R}^3$. Let $A(beta,alpha, k)$ be the corresponding scattering amplitude, $k^2$ be the energy, $alpha in S^2$ be the incident direction, $beta in S^2$ be the direction of scattered wave, $S^2$ be the unit sphere in $mathbf{R}^3$. Assume that $k=k_0 >0$ is fixed, and $alpha=alpha_0$ is fixed. Then the scattering data are $A(beta)= A(beta,alpha_0, k_0)=A_q(beta)$ is a function on $S^2$. The following invers$ textit{IP: Given an arbitrary $f in L^2(S^2)$ and an arbitrary small number $$ $q in C_0^{infty}(D)$, where $D in mathbf{R}^3$ is an arbitrary fixed domai$ $||A_q(beta)-f(beta)||_{L^2(S^2)} < epsilon$?} A positive answer to this question is given. A method for constructing such a $q$ is proposed. There are infinitely many such $q$, not necessarily real-valued." @default.
- W1694173860 created "2016-06-24" @default.
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- W1694173860 date "2013-02-02" @default.
- W1694173860 modified "2023-09-27" @default.
- W1694173860 title "Inverse scattering with the data at fixed energy and fixed incident direction" @default.
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