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Construction of reflectionless potentials with infinite discrete spectrum

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Abstract

We investigate the one-dimensional Schrödinger operator. The condition that the potential be self-similar under Darboux transformation leads to transparent potentials with infinitely many eigenvalues.

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Additional information

The authors dedicate this paper to the memory of M. C. Polivanov

Dipartimento di Fisica, Universita' di Roma “La Sapienza,” Ple. Aldo Moro 2, Roma 00185, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Roma; Landau Institute for Theoretical Physics, Moscow 117940, Russia. Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 100, No. 2, pp. 230–247, August, 1994.

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Degasperis, A., Shabat, A. Construction of reflectionless potentials with infinite discrete spectrum. Theor Math Phys 100, 970–984 (1994). https://doi.org/10.1007/BF01016760

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  • DOI: https://doi.org/10.1007/BF01016760

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