Complex energy spectra in reggeon quantum mechanics with cubic plus generalized quartic interactions

We investigate the energy eigenvalue spectra in reggeon quantum mechanics when the hamiltonian contains (non-hermitian) cubic, symmetric quartic and asymmetric quartic interactions. We describe two new methods for finding eigenvalues numerically. When the asymmetric quartic coupling is zero, the energy eigenvalue cross the vacuum state sequentially as predicted by Bronzan as long as r approx. <= 0.7. For r >= 0.7 the energy eigenvalues above the ground state pinch together pairwise above the energy axis, leaving the ground state to oscillate about the vacuum. The addition of an asymmetric quartic term appears to dilute the effects produced by increasing the cubic coupling strength. Quantitative graphs of the functional dependence of the eigenvalues on the parameter are given. An alternative derivation of Bronzan's formula for vanishing eigenvalues is given in the appendix. (orig.)