We extend the theory of Chandler, Singh, and Richardson [J. Chem. Phys. 81, 1975 (1984)] to calculate the density matrix for an excess electron in a classical liquid like bath. For a one-dimensional fluid of hard rods and for two model potentials representing the electron fluid atom interaction (one representing the excluded volume effect and the other attractive interaction), we calculate the density matrix using the values of solvent induced potential surfaces for the electron found from our earlier calculations [Phys. Rev. B 42, 6090 (1990)]. The resulting density matrix is diagonalized and values of energies and wavefunctions of the electron including the effective mass and root mean square (RMS) displacement R-beta in imaginary time beta (h) over bar. The transition of the electron to a state of self-trapping is visualized through a sudden change in the value of R-beta or the effective mass m* at a value of beta or solvent density rho(s)*. For a potential model of hard rods, we find that the RMS displacement R-beta for a given solvent density varies as (beta (h) over bar)(nu). Values of nu are evaluated for several solvent densities.