scholarly journals Eigenvalue asymptotics for the Schrödinger operator with steplike magnetic field and slowly decreasing electric potential

2003 ◽  
Vol 39 (2) ◽  
pp. 297-330 ◽  
Author(s):  
Shin-ichi Shirai
Keyword(s):  
Magnetic Field ◽  
Schrödinger Operator ◽  
Electric Potential ◽  
Schrodinger Operator ◽  
Eigenvalue Asymptotics

THE BETHE–SOMMERFELD CONJECTURE FOR THE 3-DIMENSIONAL PERIODIC LANDAU OPERATOR

2004 ◽  
Vol 16 (10) ◽  
pp. 1259-1290 ◽  
Author(s):  
DANIEL M. ELTON
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Schrödinger Operator ◽  
Electric Potential ◽  
Uniform Magnetic Field ◽  
Schrodinger Operator ◽  
Regularity Assumption ◽  
3 Dimensional

The 3-dimensional Schrödinger operator H corresponding to a uniform magnetic field and a periodic electric potential V is considered. Under the condition of magnetic flux rationality, and with a mild regularity assumption on V, it is shown that the number of gaps in the spectrum of H is finite.

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