Skip to content
中

Chapter 05

Angular momentum and spin

Pure algebra fixes every eigenvalue: the prettiest derivation in the subject.

Sections
7
Finalised
7/7
Simulations
0
Estimated time
4 hours
Read first
Chapter 03
  1. 5.1Orbital angular momentum operatorsCarry the classical L = r × p into quantum mechanics and the three components refuse to commute with each other — and that single fact determines everything about it.
  2. 5.2Angular momentum eigenvalues and spherical harmonicsClimb out every angular momentum eigenvalue from the commutation relations alone, without solving a single differential equation; then return to the sphere to see what the eigenstates look like.
  3. 5.3Spin 1/2 and the Pauli matricesThe electron carries a built-in angular momentum, but nothing is actually rotating. Three 2×2 matrices hold all of its mathematics.
  4. 5.4The Stern–Gerlach experiment, in depthA beam of silver atoms crosses an inhomogeneous magnetic field and splits in two. Chain three of these devices together and every quirk of quantum measurement steps into the open.
  5. 5.5Spin precessionIn a magnetic field a spin circles the field like a gyroscope, at a rate set by the field strength alone. A hospital MRI machine works by listening to that rate.
  6. 5.6Coupling angular momenta and Clebsch–Gordan coefficientsPut two angular momenta together and the right question is not "how do the vectors add" but "how do the four states regroup". The answer: one singlet plus one triplet.
  7. 5.7Spin–orbit couplingFrom the electron's seat, it is the nucleus that circles — and that loop of current makes a magnetic field which grabs the electron's own moment and snaps each level in two.
Start with 5.1 Orbital angular momentum operators →