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  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 80, Issue 1-2
  • January 1978, pp. 67-84

On Schrödinger's factorization method for Sturm-Liouville operators

  • U.-W. Schmincke (a1)
  • DOI: http://dx.doi.org/10.1017/S0308210500010143
  • Published online: 14 November 2011
Abstract
Synopsis

We consider the Friedrichs extension A of a minimal Sturm-Liouville operator L0 and show that A admits a Schrödinger factorization, i.e. that one can find first order differential operators Bk with where the μk are suitable numbers which optimally chosen are just the lower eigenvalues of A (if any exist). With the help of this theorem we derive for the special case L0u = −u″ + q(x)u with q(x) → 0 (|x| → ∞) the inequality

σd(A) being the discrete spectrum of A. This inequality is seen to be sharp to some extent.

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3S. Flügge Lehrbuch der theoretischen Physik, I V. Quantentheorie I. (Berlin: Springer, 1964).

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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