We present a variational method which uses a quartic exponential function as
a trial wave-function to describe time-dependent quantum mechanical systems. We
introduce a new physical variable y which is appropriate to describe the
shape of wave-packet, and calculate the effective action as a function of both
the dispersion ​ and y. The effective potential
successfully describes the transition of the system from the false vacuum to
the true vacuum. The present method well describes the long time evolution of
the wave-function of the system after the symmetry breaking, which is shown in
comparison with the direct numerical computations of wave-function.Comment: 8 pages, 3 figure