Non-Hermitian matrix description of the PT symmetric anharmonic oscillators
Abstract
Schroedinger equation H =E with PT - symmetric differential operator H=H(x) = p2 + a x4 + i β x3 +c x2+i δ x = H*(-x) on L2(-∞,∞) 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 complements and completes the recent terminating solutions as obtained for certain couplings δ at the less common negative a.
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