Electromagnetic Field Quantization & Applications to the Casimir Effect

The quantization of the electromagnetic field is demonstrated through a two-pronged approach. The classical harmonic oscillator is discussed in depth, and then its quantization is further discussed. Additionally, the classical electromagnetic field Hamiltonian is derived and analogized to the classical harmonic oscillator Hamiltonian at several points. Quantization of the electromagnetic field and its Hamiltonian are then performed, leading to an application of the free electromagnetic field energy spectrum to the analysis of the Casimir effect. This too is performed through two routes, which are by analyzing the energy gradient and by analyzing the radiation pressure of the electromagnetic field subject to certain boundary conditions; these are qualitatively different but quantitatively converge to give the same desired result.