scholarly journals Zero-Energy Bound State Decay for Non-local Schrödinger Operators

2019 ◽  
Vol 374 (3) ◽  
pp. 2151-2191 ◽  
Author(s):  
Kamil Kaleta ◽  
József Lőrinczi
Keyword(s):  
Schrödinger Operators ◽  
Bound State ◽  
Schrodinger Operators ◽  
Zero Energy ◽  
State Decay ◽  
Energy Bound ◽  
Non Local

A UNIFIED APPROACH TO RESOLVENT EXPANSIONS AT THRESHOLDS

2001 ◽  
Vol 13 (06) ◽  
pp. 717-754 ◽  
Author(s):  
ARNE JENSEN ◽  
GHEORGHE NENCIU
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Unified Approach ◽  
Zero Energy ◽  
Real Potential ◽  
Factorization Technique

Results are obtained on resolvent expansions around zero energy for Schrödinger operators H=-Δ+V(x) on L2(Rm), where V(x) is a sufficiently rapidly decaying real potential. The emphasis is on a unified approach, valid in all dimensions, which does not require one to distinguish between ∫V(x)dx=0 and ∫V(x)dx≠0 in dimensions m=1,2. It is based on a factorization technique and repeated decomposition of the Lippmann–Schwinger operator. Complete results are given in dimensions m=1 and m=2.

On ground state of some non local Schrödinger operators

2016 ◽  
Vol 96 (8) ◽  
pp. 1390-1400 ◽  
Author(s):  
Yuri Kondratiev ◽  
Stanislav Molchanov ◽  
Sergey Pirogov ◽  
Elena Zhizhina
Keyword(s):  
Ground State ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Non Local
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