01
Hilbert space, operators, Dirac notation
What is a quantum state, stripped of all pictures?
Modern · Module 12
Quantum Mechanics II — Formalism & Entanglement
The move from wave mechanics to linear algebra on Hilbert space. Once you see quantum mechanics as geometry in a complex vector space, the paradoxes become structural rather than mystical.
By the end of this module
You can work in Dirac notation, handle spin and perturbations, and state precisely what Bell ruled out.
0%0 / 7 complete
02
Angular momentum and spin
What is spinning, exactly?
03
The hydrogen atom
Can one equation produce the entire periodic table's structure?
04
Identical particles and the Pauli principle
Why does matter take up space?
05
Perturbation theory and approximation methods
What do I do when the equation cannot be solved exactly — which is almost always?
06
Entanglement and Bell's theorem
Could the particles have agreed on their answers in advance?
Primary source★ LandmarkFree
On the Einstein Podolsky Rosen Paradox ↗John S. Bell, 1964
Six pages that converted a philosophical dispute into an experiment.
Primary source★ LandmarkFree
Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? ↗Einstein, Podolsky & Rosen, 1935
The objection Bell answered.
VideoFree
Bell's Theorem: The Quantum Venn Diagram Paradox ↗minutephysics
The clearest short derivation of a Bell inequality that exists.
Check yourself
End-of-module quiz
Every answer comes with the reasoning, not just a verdict. Getting one wrong and reading why is the point.
01Spin-½ means the state returns to itself under a rotation of:
02The Pauli exclusion principle follows from:
03Bell's theorem proves that:
Answer all 3 to finish the module.