A Bayesian approach to short-time quantum dynamics: Quantum instantaneous normal modes

Described in this work is an approach to computing quantum dynamics which utilizes a conditional (Bayesian) transition probability. Using this approach the problem separates into an equilibrium and a dynamical component. The equilibrium portion of the problem is treated quantum mechanically using Fourier path integral methods, and the dynamical component is treated classically. This approach is shown to give exact quantum dynamics for polynomial potentials of orders one and zero. For more complicated problems the method is shown to be numerically exact for short-times. This Bayesian approach is then used to develop a theory for quantum instantaneous normal modes (INM's).