  We present a simple and complete variational approach to the one-dimensional
quantum Frenkel-Kontorova model. Dirac's time-dependent variational principle
is adopted together with a Hatree-type many-body trial wavefunction for the
atoms. The single-particle state is assumed to have the Jackiw-Kerman form. We
obtain an effective classical Hamiltonian for the system which is simple enough
for a complete numerical solution for the static ground state of the model.
Numerical results show that our simple approach captures the essence of the
quantum effects first observed in quantum Monte Carlo studies.
