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Dirac Notation and Hermitian Operators

Building off of the inner product notation in the last lecture, we can start using Dirac vector notation. In quantum mechanics we care about the state of a system; we denote these with ket vectors

\[| \psi \rangle\]

Commutator algebra

Outer product, projection operators, identity

Hermitian Operators

Eigenvalue Problem

Spectral Reprentation and degeneracy