Who proposed the wave equation for non-relativistic quantum mechanics?

Erwin Schrödinger proposed the wave equation for non-relativistic quantum mechanics.

The Schrödinger equation governs how a quantum system’s wavefunction changes over time. The wavefunction does not usually describe a visible physical wave; its squared magnitude gives probabilities for possible measurement outcomes. In this way, the equation predicts the evolving distribution of where a particle may be found and what values its observables may take.

Schrödinger developed the equation in 1925 and published it in 1926. His approach was inspired partly by Louis de Broglie’s matter-wave hypothesis and by the Hamiltonian formulation of classical mechanics. The equation provided a wave-based alternative to Werner Heisenberg’s matrix mechanics, although the two formulations were later shown to be mathematically equivalent.

The equation is specifically non-relativistic, so it does not fully describe particles moving near light speed or phenomena requiring particle creation and annihilation. Paul Dirac later developed relativistic quantum equations, including the Dirac equation for electrons. Max Born supplied the influential probabilistic interpretation of the wavefunction, but he did not propose the wave equation itself.