Equivalent Hermitian Hamiltonians for some non-Hermitian Hamiltonians

摘要

Six years ago, by using operator techniques and path-integral methods, it was shown that the complexnnon-Hermitian PT -symmetric Hamiltonian p2 − gx4 is equivalent to a conventional Hermitian Hamiltoniannp2 + 4gx4 − 2ˉhn√ngx. Further it was revealed that the linear term in the Hermitian Hamiltonian is anomalous innthe sense that it has no classical analog. In this paper we show that the complex non-Hermitian PT-symmetricnHamiltonian p2 − gx4 + 4iˉhn√ngx and the conventional Hermitian Hamiltonian p2 + 4gx4 + 6ˉhn√ngx have thensame eigenspectra. In this case, the anomalous terms in both Hamiltonians are different from the previous onenand vanish in the semiclassical limit. Further these equivalent Hamiltonians have zero-energy ground states. Thenexact ground-state wave functions and supersymmetric partner potentials are derived.