Non-Hermitian matrix description of the PT symmetric anharmonic oscillators
Abstract
Description
Schroedinger equation H ψ=E ψwith PT - symmetric differential operator H=H(x) = p^2 + a x^4 + i βx^3 +c x^2+i δx = 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 ψcomplements and completes the recent terminating solutions as obtained for certain couplings δat the less common negative a.
18 pages, latex, no figures, thoroughly revised (incl. title), J. Phys. A: Math. Gen., to appear
18 pages, latex, no figures, thoroughly revised (incl. title), J. Phys. A: Math. Gen., to appear