Schrodinger equation

At the center of nonrelativistic quantum mechanics, the Schrödinger equation describes how a quantum state's wavefunction changes over time. The wavefunction contains probability amplitudes, from which probabilities for measurement outcomes can be calculated. It is not itself a simple map of definite particle positions, and its meaning depends on the observable being studied. The time-dependent equation describes evolution, while its stationary form helps determine allowed energies and associated states.

These tools are essential for understanding atoms and molecules, including the structure underlying chemical bonding. Researchers and students in physics and chemistry use the equation for both single-particle models and more complicated systems. What sets it apart from classical equations of motion is that it evolves a quantum state rather than specifying one definite trajectory for every particle.