ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

11. Mathematical Physics

1991 MS Classification: 81, 34, 65 Hall, Richard L., Concordia University, Montréal, Canada Geometric spectral inversion We consider the Schrödinger operator H = −Δ+vf(x) on a suitable domain D(H) in L^{2}(R), where v > 0 is a parameter and f(x) is the potential shape which is (i) bounded below, (ii) symmetric, (iii) monotone non-decreasing for x > 0. We suppose that E_{n} = F_{n}(v), for v sufficiently large, represents the n-th discrete eigenvalue of H as a function of the ‘coupling’ parameter v. We discuss how the potential shape f can be reconstructed from one of the energy functions F_{n} alone. References: R. L. Hall, Geometric spectral inversion, J. Phys. A 28, (1995) 1771–1786; Spectral inheritance of potentials with flat bottoms, Phys. Rev. A50, (1994), 2876–2880; Geometric spectral inversion by the WKB approximation, Phys. Rev. A51 (1995), 1787–1791.