Transition state rate of escape from a one-dimensional well

2 Transition state rate of escape from a one-dimensional well 

Consider an activated rate process represented by the escape of a particle from a one-dimensional potential well. The Hamiltonian of the particle is 

Note that the fact that only half the particles move in the forward direction is taken into account in the normalization of Eq. (14.14). For a high barrier, most of the 

The transition state rate is of atypical Arrenius form a product of a frequency factor that may be interpreted as the number of attempts, per unit time, that the particle makes to exit the well, and an activation term associated with the height of the barrier. It is important to note that it does not depend on the coupling between the molecule and its environment, only on parameters that determine the equilibrium distribution. 

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