These two evolution procedures were described in a classic work by the remarkable Hungarian/American mathematician John von Neumann (1955). His ‘process 1’ is what I have termed R – ‘reduction of the state-vector’ – and his process 2 is U – ‘unitary evolution’ (which means, in effect that probability amplitudes are preserved by the evolution). In fact, there are other – though equivalent – descriptions of quantum-state evolution U, where one might not use the term ‘Schrödinger’s equation’. In the ‘Heisenberg picture’, for example, the state is described so that it appears not to evolve at all,
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U and R
