Import of Analytical Mechanics to Japan in the Age of the Birth of Quantum Mechanics

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This study examines how the Hamilton-Jacobi theory, which is part of analytical mechanics, was imported to Japan. To clarify, this study at first argues how the theory was first developed, and then further developed using quantum physics. It clarifies the various aspects of the Hamilton-Jacobi theory that worked in spectroscopy, which is related to quantum theory. During this process the theory began to evolve into a new idea. This fact exemplifies one aspect of the complexity of quantum theory and the continuity between traditional physics and quantum physics. Japanese spectroscopists, especially Yoshikatsu Sugiura, played an essential role importing the latest Hamilton-Jacobi theory to Japan.