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Keywords
(4)
Adjoint Problem
Boundary Condition
Inverse Spectral Problem
Robin Boundary Condition
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Asymptotics of eigenvalues of nonself adjoint Schr\"odinger operators on a halfline
Asymptotics of eigenvalues of nonself adjoint Schr\"odinger operators on a halfline,Kwang C. Shin
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Asymptotics of eigenvalues of nonself adjoint Schr\"odinger operators on a halfline
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Citations: 3
)
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Kwang C. Shin
We study the eigenvalues of the nonself
adjoint problem
$y^{\prime\prime}+V(x)y=E y$ on the halfline $0\leq x<+\infty$ under the
Robin boundary condition
at $x=0$, where $V$ is a monic polynomial of degree $\geq 3$. We obtain a BohrSommerfeldlike 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.
Published in 2010.
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Citation Context
(1)
...The error terms in (iii) are improved from o(1) to O � λ −ρ � in [
25
]...
Kwang C. Shin
.
Anharmonic Oscillators in the Complex Plane, symmetry, and Real Eigen...
References
(17)
Real Spectra in NonHermitian Hamiltonians Having PT Symmetry
(
Citations: 188
)
Carl M. Bender
,
Stefan Boettcher
Journal:
Physical Review Letters  PHYS REV LETT
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Analytic continuation of eigenvalue problems
(
Citations: 23
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Carl M. Bender
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Journal:
Physics Letters A  PHYS LETT A
, vol. 173, no. 6, pp. 442446, 1993
Spectral equivalences, Bethe ansatz equations, and reality properties in P Tsymmetric quantum mechanics
(
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)
Patrick Dorey
,
Clare Dunning
,
Roberto Tateo
Journal:
Journal of Physics Amathematical and General  J PHYSAMATH GEN
, vol. 34, no. 28, pp. 56795704, 2001
Analytic continuation of eigenvalues of a quartic oscillator
(
Citations: 12
)
Alexandre Eremenko
,
Andrei Gabrielov
Published in 2008.
High energy eigenfunctions of onedimensional Schrodinger operators with polynomial potentials
(
Citations: 10
)
Alexandre Eremenko
,
Andrei Gabrielov
,
Boris Shapiro
Published in 2007.
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Citations
(3)
Anharmonic Oscillators in the Complex Plane, symmetry, and Real Eigenvalues
Kwang C. Shin
Journal:
Potential Analysis
, vol. 35, no. 2, pp. 145174, 2011
Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PTSymmetry
(
Citations: 3
)
Kwang C. Shin
Journal:
Symmetry Integrability and Geometrymethods and Applications  SYMMETRY INTEGR GEOM
, 2010
Anharmonic oscillators in the complex plane, $\mathcal{PT}$symmetry, and real eigenvalues
Kwang C. Shin
Published in 2010.