  Recently O'Connell introduced an interacting diffusive particle system in
order to study a directed polymer model in 1+1 dimensions. The infinitesimal
generator of the process is a harmonic transform of the quantum Toda-lattice
Hamiltonian by the Whittaker function. As a physical interpretation of this
construction, we show that the O'Connell process without drift is realized as a
system of mutually killing Brownian motions conditioned that all particles
survive forever. When the characteristic length of interaction killing other
particles goes to zero, the process is reduced to the noncolliding Brownian
motion (the Dyson model).
