## Keywords (4)

Publications
Asymptotics of eigenvalues of non-self adjoint Schr\"odinger operators on a half-line

# Asymptotics of eigenvalues of non-self adjoint Schr\"odinger operators on a half-line,Kwang C. Shin

Asymptotics of eigenvalues of non-self adjoint Schr\"odinger operators on a half-line
We study the eigenvalues of the non-self adjoint problem $-y^{\prime\prime}+V(x)y=E y$ on the half-line $0\leq x<+\infty$ under the Robin boundary condition at $x=0$, where $V$ is a monic polynomial of degree $\geq 3$. We obtain a 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.
Published in 2010.
View Publication
 The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
 ( arxiv.org )

## Citation Context (1)

• ...The error terms in (iii) are improved from o(1) to O � λ −ρ � in [25]...

## References (17)

### Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry(Citations: 188)

Journal: Physical Review Letters - PHYS REV LETT , vol. 80, no. 24, pp. 5243-5246, 1998

### Analytic continuation of eigenvalue problems(Citations: 23)

Journal: Physics Letters A - PHYS LETT A , vol. 173, no. 6, pp. 442-446, 1993

### Spectral equivalences, Bethe ansatz equations, and reality properties in P T-symmetric quantum mechanics(Citations: 58)

Journal: Journal of Physics A-mathematical and General - J PHYS-A-MATH GEN , vol. 34, no. 28, pp. 5679-5704, 2001

### Analytic continuation of eigenvalues of a quartic oscillator(Citations: 12)

Published in 2008.

### High energy eigenfunctions of one-dimensional Schrodinger operators with polynomial potentials(Citations: 10)

Published in 2007.
Sort by:

## Citations (3)

### Anharmonic Oscillators in the Complex Plane, -symmetry, and Real Eigenvalues

Journal: Potential Analysis , vol. 35, no. 2, pp. 145-174, 2011

### Anharmonic oscillators in the complex plane, $\mathcal{PT}$-symmetry, and real eigenvalues

Published in 2010.