A practice problem for Schrödinger transmission

2003/09/24 by Zafar Ahmed, Ahmed, Zafar
Computer Science · Physics and Astronomy · #Digital Filter Design and Implementation #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0309176

10 pages, 1 figure

arxiv created 2003/09/24 · openalex publication_date 2003/09/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present the case of quantal transmission through a smooth, single-piece exponential potential, V(x)=-V₀ e^x/a, in contrast to the piece-wise continuous potentials, as a pedagogic model to demonstrate the analytic extraction of transmission (reflection) co-efficient.

Related

• Analyses of reflection and transmission at moving potential step
• Constraining transmission and reflection probabilities by using the Miller-Good transformation
• Rigorous bounds on Transmission, Reflection, and Bogoliubov coefficients
• Instantaneous Reflection and Transmission Coefficients and a Special Method to Solve Wave Equation
• Reflection probabilities of one-dimensional Schroedinger operators and scattering theory