2004/11/16 by Toshiharu Samura, Samura, Toshiharu, Masato Ohmukai +1
Physics and Astronomy · #FOS: Physical sciences #Laser-Matter Interactions and Applications #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Spectroscopy and Quantum Chemical Studies #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0411113
9 pages, 2 figures
arxiv created 2004/11/16 · openalex publication_date 2004/11/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The reflection and transmission of wave functions at a potential step is a well-known issue in a textbook of quantum mechanics. We studied the reflection and transmission characteristics analytically when the potential step is moving at a constant velocity v in the same direction as an incident wave function by means of solving the time-dependent Schrödinger equation. As for an infinite potential step, it is known that group velocity is the same as the moving velocity of the potential step. We found two interesting results when the potential step has a finite height of V0. The transmission occurs when the kinetic energy of incident wave function is larger than the effective potential hight of (√((m)/(2))v + √(V0))2. The other result is that the reflectivity depends on x, which derives from the interference between the incident and the reflected wave functions.