thesis chanced to reach Einstein, whose response was enthusiastic. Einstein stressed the importance of Broglie's work both explicitly and by building further on it. In 1925, Austrian-born physicist Wolfgang Pauli developed the Pauli exclusion principle, which states that no two electrons around a single nucleus in an atom can occupy the same quantum state simultaneously, as described by four quantum numbers. Pauli made major contributions to quantum mechanics and quantum field theory – he was awarded the 1945 Nobel Prize for Physics for his discovery of the Pauli exclusion principle – as well as solid-state physics, and he successfully hypothesized the existence of the neutrino. In addition to his original work, he wrote masterful syntheses of several areas of physical theory that are considered classics of scientific literature. In 1926 at the age of 39, Austrian theoretical physicist Erwin Schrödinger produced the papers that gave the foundations of quantum wave mechanics. In those papers he described his partial differential equation that is the basic equation of quantum mechanics and bears the same relation to the mechanics of the atom as Newton's equations of motion bear to planetary astronomy. Adopting a proposal made by Louis de Broglie in 1924 that particles of matter have a dual nature and in some situations act like waves, Schrödinger introduced a theory describing the behaviour of such a system by a wave equation that is now known as the Schrödinger equation. The solutions to Schrödinger's equation, unlike the solutions to Newton's equations, are wave functions that can only be related to the probable occurrence of physical events. The readily visualized sequence of events of the planetary orbits of Newton is, in quantum mechanics, replaced by the more abstract notion of probability. (This aspect of the quantum theory made Schrödinger and several other physicists profoundly unhappy, and he devoted much of his later life to formulating philosophical objections to the generally accepted interpretation of the theory that he had done so much to create.) German theoretical physicist Werner Heisenberg was one of the key creators of quantum mechanics. In 1925, Heisenberg discovered a way to formulate quantum mechanics in terms of matrices. For that discovery, he was awarded the Nobel Prize for Physics for 1932. In 1927 he published his uncertainty principle, upon which he built his philosophy and for which he is best known. Heisenberg was able to demonstrate that if you were studying an