Quantum states represented by vectors in Hilbert space from "summary" of The Principles of Quantum Mechanics by P. A. M. Dirac
In quantum mechanics, the state of a physical system is represented by a vector in a complex linear vector space called Hilbert space. This mathematical formalism provides a precise way to describe the properties of a quantum system and predict the outcomes of measurements. Hilbert space is a generalization of ordinary three-dimensional Euclidean space, allowing for an infinite number of dimensions. Each quantum state corresponds to a unique vector in Hilbert space, which contains all the information about the system at a given time. The vectors in Hilbert space are called state vectors or ket vectors, denoted by the symbol |ψ⟩. These vectors are normalized to unity, meaning that the inner product of a state vector with itself is equal to one. This normalization condition ensures that the probabil...
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