Fetching the paper…
Reading the bibliography…
We prove the spectral instability of the complex cubic oscillator $-\frac{d^2}{dx^2}+ix^3+i\alpha x$ for non-negative values of the parameter $\alpha$, by getting the exponential growth rate of $\|\Pi_n(\alpha)\|$, where $\Pi_n(\alpha)$ is the spectral projection associated with the $n$-th eigenvalue of the operator.
Asymptotic expansions
A. Erdelyi, · 1956
Earlier work this paper cites.
Handbook of mathematical functions
M. Abramowitz and I. Stegun, · 1964
Earlier work this paper cites.
Laplace’s method for two parameters
R. N. Pederson, · 1965
Earlier work this paper cites.
Asymptotics and special functions
F. W. J. Olver, · 1974
Earlier work this paper cites.
Perturbation theory of odd anharmonic oscillators
E. Caliceti, S. Graffi and M. Maioli, · 1980
Earlier work this paper cites.
Odd anharmonic oscillators and shape resonances
E. Caliceti and M. Maioli, · 1983
Earlier work this paper cites.
Real spectra in non-hermitian hamiltonians having 𝒫 𝒯 \mathcal{PT} -symmetry
C. M. Bender and S. Boettcher, · 1998
Earlier work this paper cites.
Eigenvalues of complex hamiltonians with 𝒫 𝒯 \mathcal{PT} -symmetry I
E. Delabaere and F. Pham, · 1998
Cited alongside, same era.
Eigenvalues of complex hamiltonians with 𝒫 𝒯 \mathcal{PT} -symmetry II
E. Delabaere and F. Pham, · 1998
Cited alongside, same era.
Spectral instability for some Schrödinger operators
A. Aslanyan and E. B. Davies, · 2000
Cited alongside, same era.
Wild spectral behaviour of anharmonic oscillators
E. B. Davies, · 2000
Cited alongside, same era.
Spectral analysis of the complex cubic oscillator
E. Delabaere and D. T. Trinh, · 2000
Cited alongside, same era.
On the reality of eigenvalues for a class of P T PT -Symmetric oscillators
K. C. Shin, · 2002
Cited alongside, same era.
Spectral asymptotics of the non-self-adjoint harmonic oscillator
E. B. Davies and A. Kuijlaars, · 2004
Later among the works it cites.
Spectra and pseudospectra
L.N. Trefethen et M. Embree, · 2004
Later among the works it cites.
On the Sturm-Liouville problem for the complex cubic oscillator
D. T. Trinh, · 2004
Later among the works it cites.
Making sense of non-Hermitian Hamiltonians
C. M. Bender, · 2007
Later among the works it cites.
Padé summability of the cubic oscillator
V. Grecchi, M. Maioli and A. Martinez, · 2009
Later among the works it cites.
On the metric operator for the imaginary cubic oscillator
D. Krejcirik and P. Siegl, · 2012
Later among the works it cites.
The spectrum of the cubic oscillator
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Asymptotique et analyse spectrale de l’oscillateur cubique
D. T. Trinh, · 2002
Cited alongside, same era.
Spectral instability for even non-selfadjoint anharmonic oscillators
R. Henry,
Cited in the paper.
V. Grecchi, and A. Martinez, · 2013
Closest in time.