Eigenfunction expansions for differential operators with operator-valued coefficients and their applications to the Schrödinger operators with long-range potentials

2005 ◽  
pp. 476-482
Author(s):  
Yoshimi Saitō
Keyword(s):  
Long Range ◽  
Differential Operators ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Eigenfunction Expansions

scholarly journals LOCALIZATION FOR ONE DIMENSIONAL LONG RANGE RANDOM HAMILTONIANS

1999 ◽  
Vol 11 (01) ◽  
pp. 103-135 ◽  
Author(s):  
VOJKAN JAKŠIĆ ◽  
STANISLAV MOLCHANOV
Keyword(s):  
Long Range ◽  
Spectral Properties ◽  
Schrödinger Operators ◽  
Pure Point ◽  
Random Schrödinger Operators ◽  
Schrodinger Operators ◽  
One Dimensional ◽  
Free Part ◽  
Random Hamiltonians

We study spectral properties of random Schrödinger operators hω=h0+vω(n) on l2(Z) whose free part h0 is long range. We prove that the spectrum of hω is pure point for typical ω whenever the off-diagonal terms of h0 decay as |i-j|-γ for some γ>8.

scholarly journals Long range scattering for higher order Schrödinger operators

2013 ◽  
Vol 254 (8) ◽  
pp. 3329-3351 ◽  
Author(s):  
Zhiwen Duan ◽  
Quan Zheng ◽  
Jing Feng
Keyword(s):  
Long Range ◽  
Schrödinger Operators ◽  
Higher Order ◽  
Schrodinger Operators
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