Non-Hermitian matrix description of the PT symmetric anharmonic oscillators

Details Non-Hermitian matrix description of the PT symmetric anharmonic oscillators Non-Hermitian matrix description of the PT symmetric anharmonic oscillators

1999-06-09

arxiv.org/abs/quant-ph/9906029v2

J.Phys.A32:7419-7428,1999

Physics

Quantum Physics

18 pages, latex, no figures, thoroughly revised (incl. title), J. Phys. A: Math. Gen., to appear

Scientific paper

10.1088/0305-4470/32/42/313

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.

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