How to Rise from Ashes : A Comprehensive Guide to Finally Understand Canonical Quantization and Build Quantum Mechanics from Scratch

Abstract: In this review essay, we account for the historical development of canonical quantization. By a detailed review of The Ultraviolet Catastrophe, The Photoelectric Effect, Compton Scattering, Matter Waves and Bohr's Atomic Model we learn about Old Quantum Theory. Through the realizations of old quantum theory we account for the development of Heisenberg-Born-Jordan Matrix Mechanics and mention in passing the development of Schrödinger's Quantum Wave Mechanics to understand how Canonical Quantization was developed by P.A.M. Dirac, which we also account for. Through Canonical Quantization we develop the Schrödinger and Heisenberg equations of motion from first principles using displacement operators to describe the Double Slit Experiment only using results contained in the essay. We conclude by stating that the three main questions posed by this essay,"How exactly did physicists figure out that classical physics was insufficient?", "Why do we use Hermitian operators in Hilbert space, and how did physicists infer the commutation relations of quantum mechanics?" and "How can the equations of motion be developed from first principles?" have been answered, albeit in realization that no universal scheme for quantizing classical theories exist, leading to recommendations for further study.