modelled as the unitary matrix , which means that when a photon meets the beam splitter it will either stay on the same path with a probability amplitude of , or be reflected to the other path with a probability amplitude of . The phase shifter on the upper arm is modelled as the unitary matrix , which means that if the photon is on the "upper" path it will gain a relative phase of , and it will stay unchanged if it is in the lower path. A photon that enters the interferometer from the left will then be acted upon with a beam splitter , a phase shifter , and another beam splitter , and so end up in the state and the probabilities that it will be detected at the right or at the top are given respectively by One can therefore use the Mach–Zehnder interferometer to estimate the phase shift by estimating these probabilities. It is interesting to consider what would happen if the photon were definitely in either the "lower" or "upper" paths between the beam splitters. This can be accomplished by blocking one of the paths, or equivalently by removing the first beam splitter (and feeding the photon from the left or the bottom, as desired). In both cases there will be no interference between the paths anymore, and the probabilities are given by , independently of the phase . From this we can conclude that the photon does not take one path or another after the first beam splitter, but rather that it is in a genuine quantum superposition of the two paths. Applications Quantum mechanics has had enormous success in explaining many of the features of our universe, with regards to small-scale and discrete quantities and interactions which cannot be explained by classical methods. Quantum mechanics is often the only theory that can reveal the individual behaviors of the subatomic particles that make up all forms of matter (electrons, protons, neutrons, photons, and others). Solid-state physics and materials science are dependent upon quantum mechanics. In many aspects modern technology operates at a scale where quantum effects are significant. Important applications of quantum theory include quantum chemistry, quantum optics, quantum computing, superconducting magnets, light-emitting diodes, the optical amplifier and the laser, the transistor and semiconductors such as the microprocessor, medical and research imaging such as magnetic resonance imaging and electron microscopy. Explanations for