Schrödinger Equation
A fundamental partial differential equation describing how the quantum wave function of a physical system evolves deterministically over time.
Governing formula
i ℏ (∂ψ / ∂t) = Ĥ ψ, Ĥ ψ = E ψ
SI unit
Energy (Eigenvalue E in Joules or eV)
In depth
Formulated by Erwin Schrödinger, this equation serves as the primary dynamical law of non-relativistic quantum mechanics. The Hamiltonian operator Ĥ represents total kinetic plus potential energy. The time-independent form yields stationary energy eigenstates and energy eigenvalues E.
Examples in the real world
Solving the time-independent Schrödinger equation for the hydrogen atom to derive exact atomic energy levels and electron orbital shapes.