Mp. Blencowe et al., APPLYING THE LINEAR DELTA-EXPANSION TO THE I-PHI(3) INTERACTION, Physical review. D. Particles and fields, 57(8), 1998, pp. 5092-5099
The linear delta expansion (LDE) is applied to the Hamiltonian H = 1/2
(p(2)+m(2)x(2))+igx(3), which arises in the study of Lee-Yang zeros in
statistical mechanics. Despite being non-Hermitian, this Hamiltonian
appears to possess a real, positive spectrum. Tn the LDE, as in pertur
bation theory, the eigenvalues are naturally real, so a proof of this
property devolves on the convergence of the expansion. A proof of conv
ergence of a modified version of the LDE is provided for the ix(3) pot
ential in zero dimensions. The methods developed in zero dimensions ar
e then extended to quantum mechanics, when we provide numerical eviden
ce for convergence.