  Quantum mechanical control of the position of a particle by using a trapping
potential-well is an important problem for the manipulation of a quantum
particle. We study the probability of successful conveyance of a particle
trapping in a potential-well, i.e., survival probability in the process
carrying of the particle for a given length within a given fixed time. For the
actual motion of conveyance, we need to accelerate the particle to move and
then decelerate it to stop at the destination. First, the relaxation of the
survival probability in a constant acceleration rate is studied in detail by
direct numerical calculation, the Wentzel-Kramers-Brillouin method, and a
method of the resonance states. The survival probability was found to show an
exponential decay in a long time, which is analyzed from a viewpoint of
eigenvalue problem. An important source of drop-off comes from a non-analytic
change of velocity at the starting point. When the rested particle begins to
move, the ground state of the rest frame is redistributed to eigenstates of the
moving frame, and then, each eigenstate of the moving frame evolves in time.
The dephasing of wavefunctions of the distributed populations reduces the
probability of successful conveyance. In general, a smooth start gives a small
initial disturbance but requires a large acceleration during the process to
reach the destination in the fixed time which causes a larger drop-off in the
process. Considering these conflicting facts, we study the survival probability
in concrete conveyance schemes. We observe the time evolution of the trapped
probability and the population distribution during the conveyance process. In
cases that the potential-well has several bound states, we propose a method to
select the particle trapped at the ground state by making use of the difference
of survival probabilities of bound states.
