Analisi del Formalismo di Dirac

We illustrate the necessity and the di?culties of developing an accurate mathematical formalism in Quantum Mechanics via a collection of known problems. Then, we proceed to a brief introduction of the mathematical en- vironment of Quantum Mechanics, which is necessary to analyze Dirac's for- malism. We compare Wave Mechanics and the Invariant representation; this study provides and insight into the foundations of their equivalency relation. Thus, we further analyze Dirac's formalism, and suggest possible solutions to the issues related to its application. Then, we observe that most of the faced problems cannot be overcome in any representation. Finally, we discuss the Hydrogen Atom and the Harmonic Oscillator, thus showing that Dirac's formalism su?ces to provide an accurate and clear description of dynamical systems.