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Examples are given of non-Hermitian Hamiltonian operators which have a real spectrum. Some of the investigated operators are expressed in terms of the generators of the Weyl-Heisenberg algebra. It is argued that the existence of an involutive operatorĴ which renders the HamiltonianĴ-Hermitian leads to the unambiguous definition of an associated positive definite norm allowing for the standard probabilistic interpretation of quantum mechanics. Non-Hermitian extensions of the PoeschlTeller Hamiltonian are also considered. Hermitian counterparts obtained by similarity transformations are constructed.

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The quark-meson coupling model due to Guichon is formulated on the basis of the independent quark model of the nucleon proposed by Bogoliubov and is applied to the phenomenological descriptions of symmetric and asymmetric nuclear matter. For symmetric matter, the model predicts, at saturation density, the incompressibility K = 335.17 MeV, the quark effective mass m * q = 238.5 MeV, and the effective nucleon mass M * = 0.76M, where M is the nucleon mass in vacuum. Neutron star masses above two solar masses are obtained.