The non PT-symmetric exactly solvable
Hamiltonian describing a system of a fermion in the external magnetic field
which couples to a harmonic oscillator through some pseudo-hermitian
interaction is considered. We point out all properties of both of the original
Mandal and the original Jaynes-Cummings Hamitonians. It is shown that these
Hamiltonians are respectively pseudo-hermitian and hermitianREF _Ref536606452 \r \h\* MERGEFORMAT [1]REF _Ref536606454 \r \h [2]. Like the direct approach to invariant vector spaces used in Refs.REF _Ref536606456 \r \h [3]REF
_Ref536606457 \r \h [4], we reveal the exact solvability of both the Mandal and Jaynes-Cummings
Hamiltonians after expressing them in the position operator and the impulsion
operator.
References
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