  A method for the experimental reconstruction of the quantum state of motion
for a single trapped ion is proposed. It is based on the measurement of the
ground state population of the trap after a sudden change of the trapping
potential. In particular, we show how the Q function and the quadrature
distribution can be measured directly. In an example we demonstrate the
principle and analyze the sensibility of the reconstruction process to
experimental uncertainties as well as to finite grid limitations. Our method is
not restricted to the Lamb-Dicke Limit and works in one or more dimensions.
