Quantum mechanics I Fall 2012 Physics 451 Quantum mechanics I Fall 2012 Nov 28, 2012 Karine Chesnel

Tuesday Nov 27 – Friday Nov 30 Quantum mechanics Test 3 Tuesday Nov 27 – Friday Nov 30 Homework HW 22 Thur Nov 29, 7pm HW 23 Tuesday Dec 4 , 7pm HW 24 Thursday Dec 6, 7pm 5

Exchange forces Attraction force Symmetrical state: Covalent bound Quantum mechanics Exchange forces Attraction force Symmetrical state: Covalent bound Repulsion force Antisymmetrical state

Two electrons Total state antisymmetrical Spin state: singulet Quantum mechanics Two electrons Total state antisymmetrical Spatial state symmetrical Spin state: singulet antisymmetrical Attraction force Covalent bound Pb 5.6

Quiz 29a If two electrons would occupy a triplet state (S=1) Quantum mechanics Quiz 29a If two electrons would occupy a triplet state (S=1) what can we say about their spatial wave function? It is antisymmetric (antibounding) It is symmetric (bounding) It could be both

Homework Pb 5.1: Pb 5.2: Pb 5.6: Quantum mechanics Reduced coordinates

Quantum mechanics Atoms e- Z=2 e- Helium Z=1 Hydrogen

Helium e- e- Quantum mechanics r2 r1 Z=2 electron 1 in the nucleus potential electron 2 in the nucleus potential Interaction between electrons 1 & 2 11

Helium Quantum mechanics To a first order: electron 2 electron 1 in the nucleus potential electron 1 in the nucleus potential 12

Helium Quantum mechanics Ground state: In this approximation: Difference comes from the missing term In the potential Experimentally: 13

Quantum mechanics Helium E Excited states: 14

Helium Symmetrization requirements Quantum mechanics Helium Symmetrization requirements Total state antisymmetric (electrons) Spatial wave function Spin state Parahelium Singlet : antisymmetric Symmetric Orthohelium Triplet : symmetric Antisymmetric

Quantum mechanics Helium Energy levels

Quiz 29b Which of these states corresponds to the energy Quantum mechanics Quiz 29b Which of these states corresponds to the energy Level 3P in 3P Orthohelium ? A. B. C. D. E. 17