10_HO_raising_lowering

Results since 1 since raising and lowering operators

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Unformatted text preview: Lowering Operator Recall ̂ Raising Operator Write the position operator in terms of the raising and lowering operators. ̂ ̂ 2 solve for 2 ∗ 2 ∗ 2 ∗ 1 ∗ 2 ∗ 2 ∗ 1 , , 0 4 9/30/2013 Selection Rules Transitions from state to ∗ have intensity, ∝ ̂ ̂ is the dipole moment operator 0, then transition is allowed 0 , then transition is forbidden If If Taylor series expansion of the dipole moment operator vs displacement ⋯ where is the dipole moment at eq. and is the change in dipole moment with vibration at equilibrium. ∗ ∗ ̂ for transition ∗ → ∗ ̂ ⋯ ∗ ∗ ⋯ ∗ , 0 when changes ⋯ ⋯ important for infrared transitions ∗ 2 2 Transitions are allowed if → ∗ ∗ 1 ∗ 1 , , 1 or Harmonic oscillator selection rule is ∆ ⋯ 1 and ⋯ ⋯ 0 1. 5 9/30/2013 Two electron convicts are sitting in a jail cell together. The first one says, "What are you in for?“ The second one says, "For attempting a forbidden transition." 6...
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