The eigenvalue and eigenvector of a non-Hermitian Hamiltonian

The non-Hermitian Hamiltonian is constructed according to the property of knots, and then the eigenvalue and corresponding eigenvector are evaluated respectively． It manifests that the eigenvalue of a non-Hermitian Hamiltonian is a complex number, and changes with the angle k and the parameter m₁． The number and position of exceptional points are obtained explicitly and graphically． Moreover, the biorthogonal normalization of the right and left eigenvectors of the non-Hermitian Hamiltonian is discussed, which is different from the case in the traditional quantum mechanics． Finally, the non-Hermitian Hamiltonian is realized experimentally in an electric circuit with resistor, inductor and capacitor components．