 where \(\ket{\psi_{1}}\) and \(\ket{\psi_{2}}\) are distinguishable states, is not the same state as a mixture of \(\ket{\psi_{1}}\) and \(\ket{\psi_{2}}\), which would be appropriate for a situation in which the state prepared was either \(\ket{\psi_{1}}\) or \(\ket{\psi_{2}}\), but we don’t know which. The difference between a coherent superposition of two terms and a mixture has empirical consequences. To see this, consider the double-slit experiment, in which a beam of particles (such as electrons, neutrons, or photons) passes through two narrow slits and then impinges on a screen, where the particles are detected. Take \(\ket{\psi_{1}}\) to be a state in which a particle passes through the top slit, and \(\ket{\psi_{2}}\), a state in which it passes through the bottom slit. The fact that the state is a superposition of these two alternatives is exhibited in interference fringes at the screen, alternating bands of high and low rates of absorption.