In the Dirac notation vectors in function space are written as |vector name>. Letting |x_o> be the delta function centered at x_o, the wave function phi(x_o) is just <x_o|phi>, i.e., a particular dot product. In Dirac notation the completeness condition is equivalent to the sum of |psi_n><psi_n| being the identity operator. A vector |phi> is called a ket, and its conjugate or dual vector <phi| is called a bra. While there is no new physics in this bra-ket notation, it is very useful in doing quantum mechanics problems, and we will be using it throughout the rest of the course.