On the discrete spectrum of a perturbed periodic Schrödinger operator

1994 ◽  
Vol 71 (1) ◽  
pp. 2269-2272
Author(s):  
S. V. Khryashchev
Keyword(s):  
Discrete Spectrum ◽  
Schrödinger Operator ◽  
Schrodinger Operator ◽  
Perturbed Periodic ◽  
Periodic Schrödinger Operator

scholarly journals Resonances for Perturbed Periodic Schrödinger Operator

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Mouez Dimassi
Keyword(s):  
Lower Bound ◽  
Schrödinger Operator ◽  
Positive Constant ◽  
Periodic Potential ◽  
Counting Function ◽  
Schrodinger Operator ◽  
Small Positive Constant ◽  
Semiclassical Regime ◽  
Perturbed Periodic ◽  
Periodic Schrödinger Operator

In the semiclassical regime, we obtain a lower bound for the counting function of resonances corresponding to the perturbed periodic Schrödinger operatorPh=-Δ+Vx+W(hx). HereVis a periodic potential,Wa decreasing perturbation andha small positive constant.

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