ISSN:
1573-0530
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract Let δ(x) be the Dirac's delta,q(x)∈L 1 (R)∩L 2 (R) be a real valued function, and λ, μ∈R; we will consider the following class of one-dimensional formal Schrödinger operators on $$L{^2} (R)\tilde H(\lambda ,\mu ) = - (d{^2} /dx{^2} ) + \lambda \delta (x) + \mu q(x)$$ . It is known that to the formal operator $$\tilde H(\lambda ,\mu )$$ may be associated a selfadjoint operatorH(λ,μ) onL 2(R). Ifq is of finite range, for λ〉0 and |μ| is small enough, we prove thatH(λ,μ) has an antibound state; that is the resolvent ofH(λ,μ) has a pole on the negative real axis on the second Riemann sheet.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00943436
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