Learn the recursive method for analyzing quantum transport in nanoelectronic devices through this 19-minute lecture from the nanoHUB-U course on Fundamentals of Nanoelectronics Part B. Explore advanced computational techniques used to calculate electronic properties in nanoscale systems where quantum effects dominate transport phenomena. Discover how the recursive method provides an efficient approach for solving complex quantum transport problems in devices with billions of nanotransistors, each containing active regions only hundreds of atoms long. Gain insights into the mathematical framework that connects atomic-scale physics to macroscopic electronic behavior, building upon concepts in non-equilibrium statistical mechanics. Examine how this computational approach contributes to understanding resistance at the atomic scale, the interconversion of electricity and heat, and fundamental thermodynamic principles in nanoelectronic systems.