A Solution of Eqs 14.62 and

To be consistent with our ansatz, that is, in order for / to be a function of the single variable u only, the coefficient oidf /du on the left-hand side should be proportional to u, that is, 

Equating the coefficients ofx and V, that is, taking F-l-y = —ayand(Wg/y = —uF and eliminating a from these equations leads to an equation for F 

Northrup, and J. A. McCammon, Stochastically gated diffusion-influenced reactions, J. Chem. Phys. 77, 4484 (1982). 

The choice between these solutions will be made by the requirements imposed by the boundary conditions. Proceeding with Eq, (14.115) in the form 

for any velocity v we require/(x oo, v) = 0. This implies that —00) = 0 (note that because T was determined to be negative, u - —00 is equivalent to x 00). Using this in (14.120) leads to 

Ben-Avraham and S. Havlin, Diffusion and Reactions in Fractals and Disordered Systems, (Cambridge University Press, Cambridge 2000). 

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