  The paper first discusses theoretically the off-resonance selective
excitation method that is dependent on the atomic internal states and used to
generate approximately a standard coherent state of harmonic oscillator. The
coherent average method then is proposed to construct the state-selective
trigger pulse. A state-selective trigger pulse can keep Gaussian shape
unchanged but change in an internal-state-dependent form the center-of-mass
position and/or momentum of an atomic Gaussian wave-packet motional state. A
Gaussian wave-packet state is one of the simplest wave-packet states that can
be easily manipulated and controlled in time and space. The paper also
investigates how to manipulate in time and space an atomic Gaussian wave-packet
motional state by a generalized quadratic potential field. A general quadratic
Hamiltonian can affect not only the center-of-mass position and momentum but
also the complex linewidth of a Gaussian wave-packet motional state while keep
Gaussian shape of the motional state unchanged. It is shown that generally
quadratic terms of a quadratic Hamiltonian can control directly the complex
linewidth, while linear terms of a quadratic Hamiltonian can affect only the
center-of-mass position and momentum of a Gaussian wave-packet motional state.
