Dirac notation

Dirac notation is a mathematical language used in quantum physics to describe states and measurements. It includes "bras" (⟨ψ|), representing the dual (proof-like) form of a state, and "kets" (|ψ⟩), representing the state itself. When combined as ⟨φ|ψ⟩, they denote the probability amplitude of transitioning from one state to another. This notation simplifies complex vector operations and helps visualize quantum interactions. Essentially, it provides a compact, standardized way to express and manipulate the properties and relationships of quantum states.