At the scale of atoms the world stops behaving like anything you have ever seen. A particle has no definite position until you look; it can be in two places at once; it tunnels through walls it hasn't the energy to climb. Quantum mechanics is the theory that tames this strangeness — not by explaining it away, but by giving a precise recipe for the probabilities, one that has never once been found wrong.
This branch builds the theory from its phenomenological roots to its full formal machinery: the
wavefunction and the Born rule, the Schrödinger equation and its solutions (wells, barriers, the
harmonic oscillator, the hydrogen atom), operators and observables, the uncertainty principle,
Dirac notation, and angular momentum and spin. Its mathematical home is the linear algebra and
differential equations in