>[!abstract] >The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. > >Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics. Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of the wave function, the quantum-mechanical characterization of an isolated physical system. The equation was postulated by Schrödinger based on a postulate of Louis de Broglie that all matter has an associated matter wave (Wikipedia, 2025). >[!related] >- **North** (upstream): [[Quantum mechanics]] >- **West** (similar): [[Heisenberg picture]] >- **East** (different): [[Classical mechanics]] >- **South** (downstream): [[Wavefunction evolution]]