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Hamilton–Jacobi
Theory of Dynamics
The Hamilton–Jacobi (H-J) theory has some advantages in the analysis of periodic motions and is
one of the methods developed for more practical problem solving. Before the advent of the modern
quantum theory, Bohr’s atomic theory was treated in terms of the H-J theory. The H-J theory also
played an important role in optics and in shaping up and deriving the Schrodinger equations.
15.1 CANONICAL TRANSFORMATION AND H-J EQUATION
The H-J equation can be derived by many means; the one from canonical transformation theory
probably is the simplest. We noted in Chapter 5 that t