Davies, E. B. Pseudo-spectra, the harmonic oscillator and complex resonances. (English) Zbl 0931.70016 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 455, No. 1982, 585-599 (1999). Summary: We prove that nonselfadjoint harmonic and anharmonic oscillator operators have nontrivial pseudospectra. As a consequence, the computation of high-energy resonances by the dilation analyticity technique is not numerically stable. Cited in 1 ReviewCited in 50 Documents MSC: 70J10 Modal analysis in linear vibration theory 34L16 Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) Keywords:resolvent norms; JWKB method; numerical stability; Schrödinger operator; anharmonic oscillator; high-energy resonances; dilation analyticity PDFBibTeX XMLCite \textit{E. B. Davies}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 455, No. 1982, 585--599 (1999; Zbl 0931.70016) Full Text: DOI