Schrödinger’s Equation: The Core of Quantum Mechanics

Schrödinger’s equation is the fundamental law describing how quantum systems evolve.
It treats particles like electrons as waves with probabilities, not fixed paths.
The wave function, 𝜓, encodes all possible outcomes of a quantum system.
Squaring the wave function gives the probability of finding a particle in a place.
The time-dependent form shows how quantum states change with time.
The time-independent form predicts stable states like atomic orbitals.
Hydrogen’s electron shells were the first triumph of Schrödinger’s equation.
It replaces Newton’s laws at microscopic scales where particles act like waves.
Quantum tunneling—particles slipping through barriers—emerges naturally from the equation.
At its heart, Schrödinger’s equation is the rulebook for the strange, probabilistic world of quantum mechanics.