The Schrödinger equation is a wave-equation-like partial differential equation (PDE) that defines the form of a function (wave function) capable of describing the quantum-mechanical characteristics of a particle or system of particles. Classical mechanics, which deals with "everyday" waves such as sound waves, offers associated wave functions which fit a somewhat similar PDE termed the (classical) wave equation. The Schrödinger equation is not quite identical to the classical wave equation, e.g., its inclusion of the term i (square root of minus 1) which implies a wave function of complex numbers. The values of the wave functions it defines map space and time to quantum mechanical amplitudes, i.e., the square root of probabilities of something occurring at that point in space and time.
Quantum mechanical calculation using the Schrödinger equation is termed wave mechanics, whereas an alternative technique using matrix mathematics is termed matrix mechanics.