How did Einstein's photoelectric effect and Schrödinger's equation collectively contribute to the development of modern technologies such as semiconductors and lasers?

Einstein’s photoelectric effect showed that light is made of photons that can knock electrons out of a material when they have enough energy, proving that light behaves in discrete packets. Schrödinger’s wave equation described how electrons move in atoms and crystals, letting scientists calculate the energy bands that determine a material’s electrical properties. Using these ideas, researchers could design p‑n junctions and control electron flow, which became the foundation of semiconductor transistors. The same quantum picture explains stimulated emission, where one photon forces an excited electron to drop to a lower level and emit a second identical photon, the principle behind lasers. Together, Einstein’s photon concept and Schrödinger’s wave mechanics gave the tools to engineer both the tiny electronic chips that power computers and the coherent light sources of lasers.