Physics / core
The quantum description
Rebuild the description of states, observables, dynamics, spin, and identical particles.
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Module 01 core
The quantum description
Rebuild the description of states, observables, dynamics, spin, and identical particles.
- 01
Quantum amplitudes and interference
Build predictions by adding complex amplitudes, then use the Born rule to find measurable probabilities.
24 min - 02
States, bases, and Hilbert space
Use inner products and basis changes to describe the same quantum state from different measurement perspectives.
26 min - 03
Observables and operators
Connect Hermitian operators, eigenvalues, and expectation values to the outcomes of a quantum measurement.
26 min - 04
Measurement and uncertainty
Calculate projective measurement updates and distinguish quantum outcome spread from instrument noise and ignorance.
28 min - 05
Schrödinger evolution and stationary states
Evolve energy components by their phases and understand when a time-dependent state has stationary measurement statistics.
29 min - 06
Potential wells and tunneling
Use boundary conditions to explain discrete bound-state energies and evanescent penetration through a finite barrier.
31 min - 07
The quantum harmonic oscillator
Solve an oscillator through ladder operators and understand zero-point energy, number states, and the limits of classical analogies.
30 min - 08
Angular momentum and rotation symmetry
Use angular-momentum commutators and quantum numbers to predict compatible components, spectra, and rotational behavior.
29 min - 09
Spin and two-level systems
Represent spin-1/2 states with Pauli matrices and Bloch coordinates, then predict orientation-dependent measurement probabilities.
29 min - 10
Identical particles and Fock space
Replace fictitious particle labels with mode occupations and distinguish bosonic enhancement, fermionic exclusion, and field-theory interpretation.
32 min