scholarly journals Schrödinger operators with $n$ positive eigenvalues: an explicit construction involving complex-valued potentials

2016 ◽  
Vol 92 (1) ◽  
pp. 7-12 ◽  
Author(s):  
Serge Richard ◽  
Jun Uchiyama ◽  
Tomio Umeda
Keyword(s):  
Schrödinger Operators ◽  
Explicit Construction ◽  
Schrodinger Operators ◽  
Complex Valued

scholarly journals Lieb–Thirring Inequalities for Schrödinger Operators with Complex-valued Potentials

2006 ◽  
Vol 77 (3) ◽  
pp. 309-316 ◽  
Author(s):  
Rupert L. Frank ◽  
Ari Laptev ◽  
Elliott H. Lieb ◽  
Robert Seiringer
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Complex Valued

scholarly journals On the Solvability Complexity Index for Unbounded Selfadjoint and Schrödinger Operators

2019 ◽  
Vol 91 (6) ◽  
Author(s):  
Frank Rösler
Keyword(s):  
Essential Spectrum ◽  
Hilbert Spaces ◽  
Selfadjoint Operator ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Selfadjoint Operators ◽  
Complexity Index ◽  
Compact Perturbations ◽  
Complex Valued

AbstractWe study the solvability complexity index (SCI) for unbounded selfadjoint operators on separable Hilbert spaces and perturbations thereof. In particular, we show that if the extended essential spectrum of a selfadjoint operator is convex, then the SCI for computing its spectrum is equal to 1. This result is then extended to relatively compact perturbations of such operators and applied to Schrödinger operators with (complex valued) potentials decaying at infinity to obtain $${\text {SCI}}=1$$SCI=1 in this case, as well.

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