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Quantum Mechanics
From the classical crisis that started it all through perturbation theory and scattering — the full mathematical framework of quantum theory.
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From Classical to Quantum Theory
The experiments and puzzles that classical physics could not explain.
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2
Math
Independent variables, bases, eigenstates, representations, kets, operators, and probability.
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3
Schrödinger Equations
The many forms of the Schrödinger equation across bases.
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4
Bound States
Potentials, wells, the hydrogen atom, and tunneling.
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Angular Momentum
Spin, orbital angular momentum, and the addition of angular momenta.
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Harmonic Oscillator
The classical and quantum harmonic oscillator, and ladder operators.
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Unbound States
Wave packets, free particles, and scattering.
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Time-Independent Perturbation Theory
Energy corrections when a small, constant perturbation is added to a solvable Hamiltonian.
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Identical Particles
Exchange symmetry, quantum statistics, and multi-electron atoms.
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Time-Dependent Perturbation Theory
Transition rates and Fermi's Golden Rule.
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Scattering
Cross sections, partial waves, phase shifts, and the Born approximation.
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12
Modern Applications
Semiconductors, entanglement, and quantum computing.
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