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Akihiro Ogura

Publications and source records attributed to Akihiro Ogura.

5 recordsLinked to original sources
arXiv2018

Analyzing collisions in classical mechanics using mass-momentum diagrams

We show the value of mass-momentum diagrams for analyzing collision problems in classical mechanics in one dimension. Collisions are characterized by the coefficient of restitution and the momentum of the interacting particles both before and after the collision. All those quantities are presented in the mass-momentum diagrams without the need to do any calculations. We also show that the same diagrams can be used to investigate collisions with respect to the center-of-mass system. In this case, also, we do not need to do any calculations to obtain the momentum. Since we give an alternative way of looking at collisions in classical mechanics, this article is aimed at undergraduate-level students.

physics.gen-ph↗
arXiv2007

Algebraic structure of the Feynman propagator and a new correspondence for canonical transformations

We investigate the algebraic structure of the Feynman propagator with a general time-dependent quadratic Hamiltonian system. Using the Lie-algebraic technique we obtain a normal-ordered form of the time-evolution operator, and then the propagator is easily derived by a simple ``Integration Within Ordered Product" (IWOP) technique.It is found that this propagator contains a classical generating function which demonstrates a new correspondence between classical and quantum mechanics.

quant-ph↗
arXiv2004

Linear Canonical Transformations and the Hamilton-Jacobi Theory in Quantum Mechanics

We investigate two methods of constructing a solution of the Schrödinger equation from the canonical transformation in classical mechanics. One method shows that we can formulate the solution of the Schrödinger equation from linear canonical transformations, the other focuses on the generating function which satisfies the Hamilton-Jacobi equation in classical mechanics. We also show that these two methods lead to the same solution of the Schrödinger equation.

quant-ph↗
arXiv2003

Moving Picture and Hamilton-Jacobi Theory in Quantum Mechanics

We propose a new picture, which we call the {\it moving picture}, in quantum mechanics. The Schrödinger equation in this picture is derived and its solution is examined. We also investigate the close relationship between the moving picture and the Hamilton-Jacobi theory in classical mechanics.

quant-ph↗