Study about Pseudo-Hermitian Matrix Exactly Solvable Hamiltonian | Chapter 02 | Novel Research Aspects in Mathematical and Computer Science Vol. 1

 It is considered the non-symmetric perfectly solvable Hamiltonian describing a system of a fermion in the external magnetic field that couples to a harmonic oscillator via some pseudo-hermitian interaction.

We highlight all of the original Mandal and Jaynes-Cummings Hamiltonians' properties. Under the combined action of the parity operator and the time-reversal operator, we show that the Mandal Hamiltonian is non hermitian and non invariant. It has been proven that the Mandal Hamiltonian is pseudo-hermitian with regard to and also [1,2], even if the previous properties are not satisfied. As a result, the original Jaynes-Cummings Hamiltonian is shown to be hermitian.

After expressing the Mandal and Jaynes-Cummings Hamiltonians in the position and impulsion operators, we show that they are both exact solvable, comparable to the direct approach to invariant vector spaces described in Refs [3,4].

Author(S) Details

Ancilla Nininahazwe
Institut de Pédagogie Appliquée, Université du Burundi, Bujumbura, Burundi.

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