Abstract
In this paper, we study the time evolution of three-states spin-1 non-Hermitian systems. The state vector of the wave function for Schrödinger equation is obtained analytically by using the Cayley–Hamilton theorem. We note that the behavior of the non-Hermitian three-states system corresponds to the Hermitian three-state system. Furthermore, the fluctuation between three-state spin-1 is periodically oscillating when the eigenvalues of the non-Hermitian system are real. Moreover, if the eigenvalues are imaginary, we explore that from our analysis and analytical solution that the probabilities’ amplitudes always grow with time for all physical parameters in the three-state, i.e. including the [Formula: see text]-symmetry non-Hermitian system. It means that the Schrödinger equation becomes the growth exponential.
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