A matrix for everything

Heisenberg's idea was original, quite different from anything which had previously been suggested. He set out to construct matrices for physical observables such as energy, momentum, position, frequency and velocity. Thus there would be an 'energy matrix', a 'position matrix' and so on.

An atom would be represented not by a physical picture, but by a purely mathematical model. Instead of thinking about electron orbits one could think of the atomic model as a matrix with rows and columns of 'empty spaces'. Each space would be filled by a number as we obtained the necessary information about that particular atom.

Applying one matrix to another in a certain defined way would give a set of numbers representing the results of experimental observation. For example, applying the 'frequency matrix' to the 'hydrogen matrix' would give the observed values of the frequencies of light emitted by hydrogen. Applying the same frequency matrix to the matrix for the sodium atom would give the spectral lines emitted by sodium, and so on.

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