Elements of Quantum Mechanics
Quantum Mechanics will be formulated assuming four postulates: Postulate 1: gives the universal model of any physical system: a Hilbert space on the field of complex numbers. Postulate 2: models the temporal evolution of a closed physical system that is not influenced by other physical systems. Postulate 3: regards the information that can be extracted (through a quantum measurement) from a quantum system at a given time instant. Postulate 4: formalizes the interaction among physical systems through a combination of multiple Hilbert spaces into a single Hilbert space. The mathematical tool of this formulation is given by the tensor product. Considering that our final objective is Quantum Communications, some aspects of Quantum Mechanics will not be further expanded, such as the consequences of Postulate 2 on the evolution of a quantum system, while other points, in particular quantum measurements (Postulate 3) will be exhaustively investigated.
KeywordsHilbert Space Quantum Mechanics Quantum System Coherent State Pure State
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