Quantum mechanics II Winter 2012 Physics 452 Quantum mechanics II Winter 2012 Karine Chesnel

Tuesday Feb 1: Homework # 7 Phys 452 Homework Tuesday Feb 1: Homework # 7 Pb 6.23, 6.24, 6.25, 6.27, 6.28 Review 1: M –W classes Test 1: Thu- Sat, testing center

The fine structure of hydrogen Phys 452 The fine structure of hydrogen Fine structure Bohr’s energy Relativistic correction + Spin-orbit coupling + E =

The fine structure of hydrogen Phys 452 The fine structure of hydrogen Bohr’s energy E = + Fine structure + Zeeman effect ? Pb 6.17 New relevant quantum numbers: n, l, s, j and mj

Zeeman effect Phys 452 Effect of an external field Bext S L e- “Classical view” e- S L Bext

Zeeman effect Phys 452 Bext S L Comparing: and e- Pb 6.20 Intermediate “Classical view” e- S L Bext Comparing: and Pb 6.20 Weak-field Strong field Intermediate field Fine structure dominates Zeeman effect dominates

Quiz 9a Phys 452 What is the best set of quantum numbers to express the weak-field Zeeman effect ? C. D. E.

Zeeman effect Phys 452 Bext S Weak -field L Good eigenstates: e- with Lande factor: Pb 6.21

Quiz 9b Phys 452 What is the best set of quantum numbers to express the strong-field Zeeman effect ? C. D. E.

Zeeman effect Phys 452 Bext S Strong -field L Good eigenstates: e- Pb 6.23,6.24

Zeeman effect Phys 452 Bext S intermediate -field L e- Clebsch-Gordan Pb 6.25

Hyperfine splitting Phys 452 Sp Se Bp electron: e- , me Proton: e+, mp “Spin – spin” interaction Magnetic interaction between the spin of the electron and the magnetic field produced by the spin of the proton at a distance

Phys 452 Hyperfine splitting Sp Se Bp electron: e- , me Proton: e+, mp

Hyperfine splitting Phys 452 Sp Se Bp Pb 6.27 electron: e- , me Proton: e+, mp 1/pa3 for =0 when l=0 Pb 6.27

Hyperfine splitting Phys 452 Sp Se Bp Pb 6.28 electron: e- , me Proton: e+, mp Two-particles system: Triplet Singulet Pb 6.28 Application to various types of particles

Hyperfine splitting Phys 452 E First observed in 1881 by Michelson Microwave - radiowave Explained in 1924 by Pauli Radiation omnipresent in the interstellar medium