Bra Ket

Bra–ket notation is a compact way to describe quantum states and their inner products. A **ket** (|ψ⟩) represents a column vector describing a quantum state, while a **bra** (⟨φ|) represents its conjugate transpose (a row vector). The inner product ⟨φ|ψ⟩ gives a complex number (like an overlap or probability amplitude), and the outer product |ψ⟩⟨φ| gives an operator.