Electronic Resource
College Park, Md.
:
American Institute of Physics (AIP)
Journal of Mathematical Physics
42 (2001), S. 2513-2530
ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
We consider the non-Hermitian Hamiltonian H=−d2/dx2+P(x2)−(ix)2n+1 on the real line, where P(x) is a polynomial of degree at most n≥1 with all non-negative real coefficients (possibly P≡0). It is proved that the eigenvalues λ must be in the sector |arg λ|≤π/(2n+3). Also for the cubic case H=−d2/dx2−(ix)3, we establish a zero-free region of the eigenfunction u and its derivative u′ and we find some other interesting properties of eigenfunctions. © 2001 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.1366328
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