High Resolution Spectroscopy

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High Resolution Spectroscopy

• Some Background Quantum Mechanics

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• Classical mechanics fails when applied to several
  microscopic phenomena
• Quantum mechanics has not been proven correct
  but, largely through spectroscopic experiments,
  it has been demonstrated to correctly describe
  microscopic behavior.

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Quantum Mechanical Methods

• Understanding molecular motion starts with a
  total energy expression
• E T V
• T kinetic energy
• V Potential energy

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Quantum Mechanical Methods

• T
• V

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Quantum Mechanical Methods

• Schrodinger observed that these expressions could
  be related to atomic and molecular energy-level
  patterns by replacing

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Quantum Mechanical Methods

• This results in the quantum mechanical
  hamiltonian

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Quantum Mechanical Methods

• The Harmonic Oscillator
• Described by a single coordinate
• Hookes Law motion described by

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Quantum Mechanical Methods

• Knowing the form of the potential, V, then allows
  us to build the classical mechanical hamiltonian
  for the HO

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Quantum Mechanical Methods

• Transform vectors to operators gives the quantum
  mechanical hamiltonian

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Quantum Mechanical Methods

• The Shrodinger Equation and Eigenfunctions and
  Eigenvalues.

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Quantum Mechanical Methods

• Bra-Ket notation

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Quantum Mechanical Methods

• Commutation of operators
• 2 types are of interest

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Quantum Mechanical Methods

• Ladder operators

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Quantum Mechanical Methods

• Basic commutation relations for the HO problem

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Quantum Mechanical Methods

• A relevant ladder operator for the HO problem

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Quantum Mechanical Methods

• We may factor the HO hamiltonian in terms of our
  ladder operator