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Separation of Motion QM

This article explores the separation of motion in quantum mechanics, specifically focusing on the separation of vibration and rotation. It discusses the equation γ = (4π/3ħc) |<n|μe|m>|^2ω(Nm-Nn)δ(ωo-ω), as well as its various components such as the square of the transition moment, frequency of light, population difference, and resonance factor. It also touches upon topics like dipole moment matrix elements, Einstein coefficients, and the Fermi's Golden Rule. Additionally, it provides information about the frequency problem and suggests a simple experiment to estimate the frequency of a light source.

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Separation of Motion QM

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  1. Separation of Motion QM

  2. Separation Vibration Rotation

  3.  = (4/3ħc) nem2 (Nm-Nn) (o-) 1 2 3 4 • Square of the transition moment nem2 • Frequency of the light  • Population difference (Nm- Nn) • Resonance factor - Dirac delta function (0) = 1

  4. Fermi’s Golden Rule  = (4/3ħc) nem2 (Nm-Nn) (o-) 1 Dipole Moment Matrix Elements

  5. Fermi’s Golden Rule  = (4/3ħc) nem2 (Nm-Nn) (o-) 1

  6. - + r μ = q.r Dipole Moments

  7. CO2 Vibrations

  8. n m Einstein Coefficients

  9.  = (4/3ħc) nem2(Nm-Nn) (o-) 1 2 3 4 • Square of the transition moment nem2 • Frequency of the light  • Population difference (Nm- Nn) • Resonance factor - Dirac delta function (0) = 1

  10. ●-----● Frequency

  11. Problem 3 Devise a simple experiment using fairly everyday things to estimate the frequency of a light source …or alternatively devise an experiment to determine the wavelength and assume c = 30000kms-1

  12.  = (4/3ħc) nem2 (Nm-Nn)(o-) 1 2 3 4 • Square of the transition moment nem2 • Frequency of the light  • Population difference (Nm- Nn) • Resonance factor - Dirac delta function (0) = 1

  13. http://en.wikipedia.org/wiki/Boltzmann_constant Boltzmann

  14. Nm = No e -∆E/kT n m where ∆E = Em – Eo o

  15. Nm = No e -∆E/kT n m where ∆E = Em – Eo o

  16. Maser

  17.  = (4/3ħc) nem2 (Nm-Nn) (o-) 1 2 3 4 • Square of the transition moment nem2 • Frequency of the light  • Population difference (Nm- Nn) • Resonance factor - Dirac delta function (0) = 1

  18. Dirac delta function δ(0) • Infinitely high • Infinitely narrow • Area = unity

  19. Resonance commons.wikimedia.org

  20. Millennium Bridge

  21. Tacoma

  22. ABC Rotation of a Diatomic Molecule

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