Research on the historical development of analytical mechanics that was applicable to the old quantum theory
Project/Area Number 
17500686

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Sociology/History of science and technology

Research Institution  Nihon University 
Principal Investigator 
NAKANE Michiyo Nihon University, College of Science and Technology, Research Fellow, 理工学部, 研究員 (30212088)

CoInvestigator(Kenkyūbuntansha) 
UEMATSU Eisui Nihon University, College of Science and Technology, Professor, 理工学部, 教授 (70184968)
NAKA Shigefumi Nihon University, College of Science and Technology, Professor, 理工学部, 教授 (60120515)

Project Period (FY) 
2005 – 2006

Project Status 
Completed (Fiscal Year 2006)

Budget Amount *help 
¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)

Keywords  quantum mechanics / celestial mechanics / analytical mechanics / history of physics / history of mathematics / 前川量子論 / 前期量子論 
Research Abstract 
This research examines the historical process that the socalled HamiltonJacobi theory, whose prototype was established in the middle of nineteenth century, became applicable to the old quantum theory. Among the various aspects of this theory we highlight is the notion of the canonical transformation. The canonical transformation was one of the most important essential factors for the application of the theory to the old quantum theory. We note that the HamiltonJacobi theory was effectively used not in physics but in celestial mechanics in the nineteenth century. By examining some articles of the celestial mechanics published just before the birth of the old quantum theory, we find the following facts: It was Poincare that first mentioned the relation between the canonical transformation and the complete solution of the HamiltonJacobi theory in his large work of Mecanique Celeste published in 189299.Charlier gave an exact proof of this relation in his Mechanik des Himmel in 1902 and 1907. He in fact transformed the canonical equations of motion and showed how the angular variables, which often used in celestial dynamics, become the canonical elements. Schwarzschild referred to this result and succeeded in constructing the action and angular momentum that provided appropriate mathematical tools for explaining the Stark effects. Schwarzschild's new canonical variables effectively used in explaining the old quantum theory were essentially derived from the results of celestial mechanics.

Report
(3 results)
Research Products
(5 results)