States by Wave Functions

A SOMEWHAT formidable array of rules has been laid down for the description of microscopic phenomena. Some further consideration of their status in relation to directly ascertainable experimental facts is now called for. 

We remember that one of the principal objects of scientific interpretation is the relating of the unknown to the known. The description of atoms and molecules in terms of everyday macroscopic objects having proved inadequate, they are to be described in terms of a mathematical formalism constituting the new known to which the unknown is to be referred. The success of the process can be gauged only by reasonably wide experience. 

Given that atomic systems are to be represented by wave functions obeying a special kind of differential equation, it is perhaps best to go to the heart of the matter and start by considering some general rules about the types of wave function which are in fact required for the purpose. 

Suppose a system to consist of two dissimilar particles, which may be designated 1 and 2. In the first instance they may be considered as quite independent, neither exerting any influence on the energy of the other. The states of particle 1 are defined by the equation 

When the two particles are considered together, the wave equation assumes the form 

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