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Physics 451

Study the concepts of attraction and repulsion forces in quantum mechanics, specifically in symmetrical and antisymmetrical states. Explore the spatial and spin states of electrons, as well as the energy levels in Helium.

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Physics 451

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

  2. Homework Quantum mechanics Test 3 Tuesday Nov 27 – Friday Nov 30 • HW 22ThurNov 29, 7pm • HW 23 Tuesday Dec 4 , 7pm • HW 24 Thursday Dec 6, 7pm

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

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

  5. 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

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

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

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

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

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

  11. Helium E Quantum mechanics Excited states:

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

  13. Quantum mechanics HeliumEnergy levels

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

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