Part I, Chapter 4 | Page 1 of 6
Dirac Notation
Elegant bra-ket formalism for quantum mechanics
4.1 Bras and Kets
Paul Dirac introduced an elegant notation that makes quantum mechanics calculations much simpler.
Kets $|\psi\rangle$ represent state vectors in Hilbert space.
Bras $\langle\psi|$ represent elements of the dual space.
$$\langle\phi|\psi\rangle = \text{inner product}$$
Key Concepts
- • Kets $|\psi\rangle$ are vectors, bras $\langle\psi|$ are dual vectors
- • Inner product: $\langle\phi|\psi\rangle$
- • Outer product: $|\psi\rangle\langle\phi|$ is an operator