Schrödinger's Equation

References

• “Quantum Mechanics”, David McIntyre

Physics theories are judged on their predictive power. Classical mechanics relies on Newton’s second law to predict the future of a particles’ motion. The ability to predict the quantum future started with Erwin Schrödinger and bears his name.

The time evolution of a quantum system is governed by the differential equation

$$i\hslash \frac{d}{dt}|\psi (t)⟩=H(t)|\psi (t)⟩$$

where the operator $H$ corresponds to the total energy of the system and is called the Hamiltonian operator of the system because it is derived from the classical Hamiltonian. This equation is known as the Schrödinger equation.