Abstract: This paper incorporates the discussion of nonHermitian quantum systems into the exploration and practice of quantum mechanics teaching reform. It decomposes the matrix of nonreciprocal Hamiltonian into Hermitian Hamiltonian and nonreciprocal perturbation, and uses nondegenerate perturbation method to solve the energy eigenvalues and eigenstates. It is found that the obtained results are completely consistent with the results obtained by directly diagonalizing the nonreciprocal Hamiltonian and expanding it to secondorder approximation. This indicates that there is a certain connection between non reciprocal Hamiltonian and Hermitian quantum theory.   We believe that the results of this work will help further understand the physical properties of nonreciprocal Hamiltonian.

Key words: nonreciprocal, Hamiltonian, diagonalizing, non-degenerate perturbation