Generating converging bounds to the (complex) discrete states of the P2 + iX3 + iαX Hamiltonian

The eigenvalue moment method (EMM) is applied to the Hα≡P2 + iX3 + iαX Hamiltonian, enabling the algebraic/numerical generation of converging bounds to the complex energies of the L2 states, as argued (through asymptotic methods) by Delabaere and Trinh. The robustness of the formalism, and its computational implementation, suggest that the present non-negativity formulation implicitly contains the key algebraic relations by which to prove Bessis' conjecture that the eigenenergies of the H0 Hamiltonian are real. The required algebraic analysis of the EMM procedure pertaining to this problem will be presented in a forthcoming paper.

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