On Eigenfunction Decay for Two Dimensional¶Magnetic Schrödinger Operators
✍ Scribed by H. D. Cornean; G. Nenciu
- Publisher
- Springer
- Year
- 1998
- Tongue
- English
- Weight
- 170 KB
- Volume
- 192
- Category
- Article
- ISSN
- 0010-3616
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📜 SIMILAR VOLUMES
We prove the WKB asymptotic behavior of solutions of the differential equation &d 2 uÂdx 2 +V(x) u=Eu for a.e. E>A where V=V 1 +V 2 , V 1 # L p (R), and V 2 is bounded from above with A=lim sup x Ä V(x), while V$ 2 (x) # L p (R), 1 p<2. These results imply that Schro dinger operators with such poten
## Abstract The zero set {__z__∈ℝ^2^:ψ(__z__)=0} of an eigenfunction ψ of the Schrödinger operator ℒ︁~__V__~=(i∇+**A**)^2^+__V__ on __L__^2^(ℝ^2^) with an Aharonov–Bohm‐type magnetic potential is investigated. It is shown that, for the first eigenvalue λ~1~ (the ground state energy), the following