Mathematical and Physical Model of the Generation and the Transmission of Single Photon and Its Quantum State Representations

From Maxwell equation group, considering the mass of photon m, a two-dimensional finite difference time domain (FDTD) recursive formula is derived, the mathematical physical model of photon transmission is established, and the process of photon generation is simulated successfully. Based on the hypothesis of TE
_Z
wave transmission, the process of photon transmission along the Z axis is given without considering the mass of the photon, producing the spin entangle between two photons. In the case of considering photon mass, a velocity component is generated which perpendicular to the propagation direction, resulting in the angular momentum of the orbit, thus causing a new entanglement. Moreover, the image of the photon entanglement and the quantum state representation of two entangled photons are obtained. Also, the quantum state generated by the angular momentum of the photon orbit cannot be equivalent to linear polarization when the velocity component perpendicular to the direction of propagation exceeds 0.3 times of the speed of light in the vacuum, a quantum state representation of the single photon twist needs to be further found.