Non-Hermitian matrix description of the PT symmetric anharmonic oscillators
Quantum Physics
2008-11-26 v2
Abstract
Schroedinger equation H \psi=E \psi with PT - symmetric differential operator H=H(x) = p^2 + a x^4 + i \beta x^3 +c x^2+i \delta x = H^*(-x) on L_2(-\infty,\infty) is re-arranged as a linear algebraic diagonalization at a>0. The proof of this non-variational construction is given. Our Taylor series form of \psi complements and completes the recent terminating solutions as obtained for certain couplings \delta at the less common negative a.
Keywords
Cite
@article{arxiv.quant-ph/9906029,
title = {Non-Hermitian matrix description of the PT symmetric anharmonic oscillators},
author = {Miloslav Znojil},
journal= {arXiv preprint arXiv:quant-ph/9906029},
year = {2008}
}
Comments
18 pages, latex, no figures, thoroughly revised (incl. title), J. Phys. A: Math. Gen., to appear