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Lecture 5. A QM Model for Rotational Motion

Lecture 5. A QM Model for Rotational Motion. References. Engel, Ch. 7 Molecular Quantum Mechanics, Atkins & Friedman (4th ed. 2005), Ch. 3 Introductory Quantum Mechanics, R. L. Liboff (4 th ed, 2004), Ch. 7 A Brief Review of Elementary Quantum Chemistry

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Lecture 5. A QM Model for Rotational Motion

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  1. Lecture 5. A QM Model for Rotational Motion References • Engel, Ch. 7 • Molecular Quantum Mechanics, Atkins & Friedman (4th ed. 2005), Ch. 3 • Introductory Quantum Mechanics, R. L. Liboff (4th ed, 2004), Ch. 7 • A Brief Review of Elementary Quantum Chemistry • http://vergil.chemistry.gatech.edu/notes/quantrev/quantrev.html • Wikipedia (http://en.wikipedia.org): Search for • Polar coordinate system // Spherical coordinate system • Particle on a ring // Particle on a sphere

  2. Particle on a Ring: Free Rotation in 2 Dimension

  3. Particle on a Ring: Free Rotation in 2 Dimension

  4. r0 = -m l2  Particle on a Ring: Free Rotation in 2 Dimension

  5. Particle on a Ring: Eigenfunction Normalization

  6. Particle on a Ring: Boundary Condition Wave functions must be single-valued:

  7. Particle on a Ring: Final Solutions Doubly degenerate except for ml = 0 Real parts of wave functions No zero point energy: Energy can be zero.

  8. Particle on a Ring: Summary Schrödinger eqn. B.C Wave Functions The wave function have to be single-valued Energy Levels

  9. Summary

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