Computational Methods and Function Theory

, Volume 10, Issue 1, pp 111–133 | Cite as

Asymptotics of Eigenvalues of Non-Self-Adjoint Schrödinger Operators on a Half-Line



We study the eigenvalues of the non-self-adjoint problem
$$ - y^{\prime \prime}+V(x)y=Ey$$
on the half-line 0 ≤ x < +∞ under the Robin boundary condition at x = 0, where V is a monic polynomial of degree at least 3. We obtain a Bohr-Sommerfeld-like asymptotic formula for E n that depends on the boundary conditions. Consequently, we solve certain inverse spectral problems, recovering the potential V and boundary condition from the first (m + 2) terms of the asymptotic formula.


Non-self-adjoint Schrödinger operators Robin boundary condition asymptotics of eigenvalues 

2000 MSC

34L20 34L40 


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Copyright information

© Heldermann  Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of West GeorgiaCarrolltonUSA

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