where ϕ ϕ α α ( x ) = ⟨ ⟨ x | α α ⟩ ⟩ is the projection of the state into the | x ⟩ ⟩ basis and is called the wave function of the particle. In both instances we notice that | α α ⟩ ⟩ can be expanded as a superposition of an infinite number of basis states.