Approximations of spectra of Schrödinger operators with complex potentials on ℝd

Bögli, Sabine; Siegl, Petr; Tretter, Christiane (2017). Approximations of spectra of Schrödinger operators with complex potentials on ℝd. Communications in partial differential equations, 42(7), pp. 1001-1041. Taylor & Francis 10.1080/03605302.2017.1330342

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We study spectral approximations of Schrödinger operators T = −Δ+Q with complex potentials on Ω = ℝd, or exterior domains Ω⊂ℝd, by domain truncation. Our weak assumptions cover wide classes of potentials Q for which T has discrete spectrum, of approximating domains Ωn, and of boundary conditions on ∂Ωn such as mixed Dirichlet/Robin type. In particular, Re Q need not be bounded from below and Q may be singular. We prove generalized norm resolvent convergence and spectral exactness, i.e. approximation of all eigenvalues of T by those of the truncated operators Tn without spectral pollution. Moreover, we estimate the eigenvalue convergence rate and prove convergence of pseudospectra. Numerical computations for several examples, such as complex harmonic and cubic oscillators for d = 1,2,3, illustrate our results.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Bögli, Sabine; Siegl, Petr and Tretter, Christiane

Subjects:

500 Science > 510 Mathematics

ISSN:

0360-5302

Publisher:

Taylor & Francis

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

17 Apr 2018 10:28

Last Modified:

23 Oct 2019 08:46

Publisher DOI:

10.1080/03605302.2017.1330342

BORIS DOI:

10.7892/boris.109168

URI:

https://boris.unibe.ch/id/eprint/109168

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