IVD3. The Variational Principle.

There is a variational principle associated with every linear (partial differential) equation.  If we let

(IVD3-1)  

with  defined to give a suitable scalar product, then

(IVD3-2)   

We speculate that this associated variational problem is the origin of the variational principle in quantum mechanics, but we do not see how to show this at the present time.  The demonstration of the connection will presumably involve a good understanding of the Heisenberg picture and of the conversion of operators to field theoretic form.