the Meyer-Miller mapping model, which exactly maps discrete quantum states onto a fictitious set of harmonic oscillator raising and lowering operators, has found great utility as a starting point for several semiclassical quantum dynamics algorithms.

\[ | \alpha \rangle \rightarrow \hat{a}^\dagger_\alpha = \frac{1}{\sqrt{2}}(\hat{x}_\alpha - i \hat{p}_\alpha) \]

where we have set \( \hbar \) and the arbitrary mass and frequency to 1. The great convenience of this representation is that it allows for a consistent continuous dynamical platform on which to propagate all degrees of freedom.

Reference List:

• A classical analog for electronic degrees of freedom in nonadiabatic collision processes
  H.-D. Meyer and W. H. Miller
  The Journal of Chemical Physics  70    (1979)
  
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