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Non-Hermitian matrix description of the PT symmetric anharmonic oscillators

Miloslav Znojil
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Abstract

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.

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Miloslav Znojil. 1999-09-07. Non-Hermitian matrix description of the PT symmetric anharmonic oscillators. https://doi.org/10.1088/0305-4470%2F32%2F42%2F313

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