In this paper, we developed several new methods to describe a photon’s emission and propagation process: 1) To explain a photon that emitted from a Bohr atom from the n=3 to n=2 electron orbit transition, we added a virtual electron that doing RF rotation in a virtual 2D orbit with n=2.43, and it can intuitively explain the frequency and the transverse wave of the photon; 2) Using the newly designed {N,n} QM field theory and the non-Born probability (NBP), we described the photon’s emission and propagation process as a series excitation of a {N,n} QM field’s nLL QM state from low n to high n (e.g., from the {N,n} QM field’s ground state n=1, or |1,0,0> to the first excited state n=2, or |2,1,1>, then to the second excited n=3, or |3,2,2>, and then to the third excited state n=4, or |4,3,3>, …). To describe a photon (that propagated to high n in the {N,n} QM field) with a limited size, in the NBP density formula (of the nLL QM state in the {N,n} QM field), we used the multiplier n’ for the exponential index so that we can describe a photon with any appropriate size that we want; 3) We hypothesized that a photon has an onion-like multi-shells physical structure (a superposition of many QM states), and has a “standard” size of about 100x of its wavelength. We explained a photon’s wave-particle duality as that its out-shells have the wave character, while its inner core has the particle character. We explained a photon’s double-slit experiment as that its out-shell wave’s interference guided its inner core’s particle motion; 4) We explored the possibility that whether the redshift (with Hubble’s constant ~ 70 (km/s)/Mpc) is the natural attribute of the photon propagation; 5) Alternatively, we used only two QM states to describe a photon’s emission and propagation: the ground state of {N,n} QM field |1,0,0> and the excited state of {N,n} QM field |2,1,1>, with r1 = c * t, so that the speed of the light c is incorporated into the description. 6) We believe that the {N,n} QM field theory can be used for other particles’ description as well. Finally, we explained the physical meaning of the matter wave’s wave function as the NBP 3D distribution of a particle/celestial body’s movement trajectory (that is described by the Schrodinger equation).