|Abstract||Erwin Schroedinger and Werner Heisenberg were the originators of two approaches, known respectively as “wave mechanics” and “matrix mechanics”, to what is now called “quantum mechanics’ or “quantum theory”. The two approaches appear to be extremely different, both in their technical forms, and in their philosophical underpinnings. Heisenberg arrived to his theory by effectively renouncing the idea of trying to represent a physical system, such as a hydrogen atom for example, as a structure in space-time, but by instead, following the lead of Einstein’s 1905 theory of relativity, representing only empirically observable properties, such as the transition amplitudes between the stationary states of the atom. These amplitudes can be arranged in square arrays of numbers. In Heisenberg’s scheme these arrays, and other like them, are combined according to certain rules that were later recognized by Max Born to be the rules of matrix multiplication. The whole scheme is abstract and mathematical, and avoids using any space-time picture of what is going on at the atomic level. Schroedinger, on the other hand, represented the electron in an atom by a cloudlike wave surrounding the nucleus. This is a space-time structure that, superficially at least, is more in line with the classical physical theories of the eighteenth and nineteenth centuries|
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