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Construction of reflectionless potentials with infinite discrete spectrum. (English) Zbl 0857.34073
Theor. Math. Phys. 100, No. 2, 970-984 (1994) and Teor. Mat. Fiz. 100, No. 2, 230-247 (1994).
Summary: We investigate the one-dimensional Schrödinger operator. The condition that the potential be self-similar under Darboux transformations leads to transparent potentials with infinitely many eigenvalues.

MSC:
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81U30 Dispersion theory, dispersion relations arising in quantum theory
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