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Quantum Mechanics: Spin and Angular Momentum in Elementary Particles

This physics course covers the principles of quantum mechanics, focusing on spin and angular momentum in elementary particles. Topics include spin types, representation of angular momentum, Clebsch-Gordan coefficients, and the relationship between spin and magnetic field. Homework assignments and practice tests are provided.

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Quantum Mechanics: Spin and Angular Momentum in Elementary Particles

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  1. Physics 451 Quantum mechanics I Fall 2012 Nov 16, 2012 Karine Chesnel

  2. Quantum mechanics Announcements • Homework this week: • HW #20 Thursday Nov 17 by 10pm • Pb 4.27, 4.28, 4.29, 4.33, 4.34, 4.35 Practice Test 3 review Mon Nov 19 – Tu Nov 20 Test 3 : Monday Nov 26 – Friday Nov 30

  3. orbital spin Quantum mechanics The Spin Types of angular momentum

  4. Representation of Quantum mechanics Agular moment in the atom • Orbital moment (l) • Spin moment (s)

  5. Fermions: (S half-integer) S=1/2 Leptons: electrons,… Quarks: u,b,c,s,t,b • Bosons: (S integer) Photon S=1 Quantum mechanics Spin in elementary particles Each elementary particle is characterized by an immutable spin S Proton, neutron Mesons

  6. Quantum mechanics The spin

  7. Quantum mechanics The spin

  8. Spin up Spin down Quantum mechanics The spin 1/2 The “spinor”

  9. Quantum mechanics Pauli matrices Pb 4.29

  10. Normalization Expectation values etc… Quantum mechanics State of the electron Pb 4.27, 4.28, 4.29

  11. A. 0 • B. • D. • E. Quantum mechanics Quiz 29a When measuring Sx on an electron, what are the possible results?

  12. Possibilities for two spins 1/2 Quantum mechanics Adding spins

  13. Triplet Singlet Quantum mechanics Adding spins 1/2 possibilities

  14. Triplet Singulet Quantum mechanics Adding spins 1/2 Magnitude of the spin momentum ?

  15. Possible values for S: Clebsch- Gordan coefficients Quantum mechanics Adding spins S Pb 4.34, 4.35

  16. Quantum mechanics Clebsch- Gordan coefficients

  17. A. • B. • D. • E. Quantum mechanics Quiz 29b What is the value of the Clebsch-Gordan coefficient ?

  18. S Quantum mechanics The spin and magnetic field

  19. S B Quantum mechanics The spin and magnetic field

  20. z a y x Larmor frequency Quantum mechanics Larmor precession B S Pb 4.32

  21. S Quantum mechanics Stern-Gerlach experiment z B Moves down Moves up

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