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It is shown that the generalized Schrödinger equation can be obtained by a transition from the relativistic analog of Hamilton's problem.

From the theory of relativity, the following expression is known for the differential of the action function:

where

The generalized momenta are given by

It follows:

On the other hand:

also

Let's make an assumption similar to Schrödinger's that equation (5) is the limit of a linear equation for