Time-independent Schrödinger Equation

The time-independent Schrödinger equation is a fundamental formula in quantum mechanics that describes the behavior of particles like electrons in a stable system. It essentially tells us how the particle's energy relates to its wavelike nature and the forces acting on it. Solving this equation gives us the possible energy levels and corresponding probability distributions—indicating where the particle might be found. It’s key for understanding atomic and molecular structures, providing a mathematical framework that predicts the behavior of quantum systems without considering changes over time.