A completeness relation is an expression that ensures a complete set of basis states in a vector space, which allows any state to be represented as a linear combination of these basis states. This concept is crucial in quantum mechanics, particularly when dealing with Hermitian operators, as it guarantees that measurements can be fully described within the framework of the state space. The completeness relation is often expressed mathematically as $$ ext{I} = \sum_{n} |n\rangle \langle n|$$, where $$|n\rangle$$ are the basis vectors and $$\text{I}$$ is the identity operator.
congrats on reading the definition of completeness relation. now let's actually learn it.