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Inverse problem from the discrete spectrum in the D = 2 dimensional space

Abstract : Considering the Schrödinger equation in the D = 2 dimensional space, we propose a method to determine a circular symmetric potential from its discrete spectrum. The approach is based on the relationships between the moments of the ground state density and the lowest excitation energy of each angular momentum. The required condition for a unique answer is the knowledge of all the lowest eigenvalues. In principle, it means an infinite number of moments to be known. As we shall show, reasonable accuracy can be reached in practice with a finite set of moments. Two illustrative examples are presented.
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http://hal.in2p3.fr/in2p3-01098188
Contributor : Sophie Heurteau <>
Submitted on : Tuesday, December 23, 2014 - 11:21:58 AM
Last modification on : Wednesday, September 16, 2020 - 4:08:37 PM

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R. J. Lombard, R Yekken. Inverse problem from the discrete spectrum in the D = 2 dimensional space. Physica Scripta, IOP Publishing, 2014, 89, pp.085201. ⟨10.1088/0031-8949/89/8/085201⟩. ⟨in2p3-01098188⟩

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