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Spectral deformations of one-dimensional Schrödinger operators

Gesztesy, F. and Simon, B. and Teschl, G. (1996) Spectral deformations of one-dimensional Schrödinger operators. Journal d'Analyse Mathématique, 70 (1). pp. 267-324. ISSN 0021-7670. doi:10.1007/BF02820446.

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We provide a complete spectral characterization of a new method of constructing isospectral (in fact, unitary) deformations of general Schrödinger operators H =− d^2/dx^2 + V in H =− d^2/dx^2 + VinL^2(ℝ). Our technique is connected to Dirichlet data, that is, the spectrum of the operator H^D on L^2((−∞,x_0)) ⊕ L^2((x_0, ∞)) with a Dirichlet boundary condition at x_0. The transformation moves a single eigenvalue of H^D and perhaps flips which side of x_0 the eigenvalue lives. On the remainder of the spectrum, the transformation is realized by a unitary operator. For cases such as V(x) → ∞ as |x| → ∞, where V is uniquely determined by the spectrum of H and the Dirichlet data, our result implies that the specific Dirichlet data allowed are determined only by the asymptotics as E → ∞.

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Simon, B.0000-0003-2561-8539
Additional Information:© 1996 Hebrew University of Jerusalem. Received July 15, 1996. This material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The Government has certain rights in this material.
Funding AgencyGrant Number
Subject Keywords:Jacobi Operator; Dirichlet Eigenvalue; Dirichlet Data; Double Commutation; Isospectral Deformation
Issue or Number:1
Record Number:CaltechAUTHORS:20180315-135902699
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Official Citation:Gesztesy, F., Simon, B. & Teschl, G. J. Anal. Math. (1996) 70: 267.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85341
Deposited By: Ruth Sustaita
Deposited On:16 Mar 2018 16:20
Last Modified:15 Nov 2021 20:27

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