Matrix Mechanics and Wave Mechanics.

Between Planck's explanation of black-body radiation in 1899 and 1925 numerous ideas were put forth to explain quantum effects. None of them could be used as a new basis for mechanics, and replace Newton's laws of motion, however. Then in a few months not one but two theories were published that agreed with experiments, and that did form the foundation of quantum physics.

Matrix mechanics

At the end of 1925 Werner Heisenberg, in collaboration with Born and Jordan, proposed a radical departure from thinking about atoms in terms of electrons moving around nuclei. He argued that this would lead only to flawed theories, because this is not how atoms really are. Instead he said that one should concentrate only on experimental results. If a theory could predict these results, then it should be accepted. His theory replaces physical quantities like coordinates of particles, momenta, and energies by matrices, and is therefore called matrix mechanics. Rules for manipulating these matrices then lead to prediction that can be compared to experiments.

Although matrix mechanics agreed with experiments it was not a popular theory. Matrices may now be part of the mathematics that are taught to physics and chemistry students at universities in their first year, but in 1925 few non-mathematicians had heard of them. Moreover they had an odd property. If two physical properties, say A and B, are multiplied with each other, one would expect AB=BA. If these properties are replaced by matrices, then this suddenly is not necessarily true.

Wave mechanics

In the beginning of 1926 Erwin Schrödinger proposed another theory. His work was based on the Hamilton-Jacobi formulation of classical mechanics. In this formulation the behavior of particles is described by a wave equation. A clever change of this equation led to what's now called the Schrödinger equation. It too agreed well with experiments. A system, for example an atom or molecule, is described by a so-called wave function in Schrödinger's theory, and the theory is called wave mechanics. It was much more readily accepted then matrix mechanics, in part because the wave function could be visualized, and the theory was based on well-established classical mechanics.

Modern quantum mechanics

Matrix mechanics and wave mechanics predict exactly the same results for experiments. This suggests that they are really different forms of a more general theory. In 1930 Paul Dirac showed that this is indeed the case. He gave a more general formulation of quantum mechanics; the one that is still used today. Matrix and wave mechanics can be derived from this formulation, and are then called the Heisenberg and the Schrödinger picture, respectively. Other pictures can also be derived. Which picture one actually uses in practice depends on which one is the most convenient to work with. In quantum chemistry the Schrödinger picture is generally the easier.