  We find a set of new exact solutions of a quantum harmonic oscillator, which
describes some wave-packet trains with average energy being proportional to
both the quantum level and classical energy of the oscillator. Center of the
wave-packet trains may oscillate like a classical harmonic oscillator of
frequency $\omega$. Width and highness of the trains may change simultaneously
with frequency $2 \omega $ as an array of breathers. Under some perturbations
the wave-packet trains could transit between the states of different quantum
numbers. We demonstrate analytically and numerically that the wave-packet
trains can be strictly fitted to the matter-wave soliton trains observed by
Strecher et al. and reported in Nature 417, 150(2002). When the wave-packets
breathe with greater amplitudes, they show periodic collapse and revival of the
matter-wave.
