Concluding remarks on the general equations

Thus far we have developed equations that are not restricted to particular systems, although in the main we have kept to systems that are in stationary states. These are systems having energy that is precise and unchanging in time. 

A great deal more could be said in general nothing has been said of the uncertainty principle, for example. The postulates of quantum mechanics have not been exhausted by those presented in this chapter. However, at this point we take up particular examples, in the belief that the skeleton presented so far will be less repulsive if it is fleshed out a bit. 

Finally, a remark or two about the treatment at the end of Chapter 19, which attempts to relate the classical wave equation and the Schrodinger equation. It should be clear that whether or not the Schrodinger equation is correct depends only on its predictions of behavior and not in the least on whether or not there is some means of transforming the classical wave equation into the Schrodinger equation. On the other hand, the Schrodinger treatment of a system is required to reduce to Newtonian mechanics in the limit as Planck s constant approaches zero, or in the limit of large masses and distances. Suffice it to say that the Schrodinger equation does reduce properly in these circumstances. 

In passing, it should be mentioned that since 1is a probability per unit volume, it follows that ij/ has dimension (length) in three-dimensional space. For a one-dimensional problem, the volume element is simply a length, so the dimension of ij/ is (length)  

1 What are the consequences for measurement when two operators commute When they do not commute  

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