TITLE:
Pseudo-Hermitian Matrix Exactly Solvable Hamiltonian
AUTHORS:
Ancilla Nininahazwe
KEYWORDS:
Pseudo-Hermiticity, Exact Solvability, Direct Method
JOURNAL NAME:
Open Journal of Microphysics,
Vol.9 No.1,
January
31,
2019
ABSTRACT: 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 hermitian REF _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.