  We develop a class of traveling-envelope solutions of Schr\"odinger equation
for a free particle whose amplitude is moving with constant group velocity
while keeping its shape undistorted. We show that solution with arbitrary
finite group velocity is obtained by Lorentz boosting the solution with
vanishing group velocity, if the quantum average energy $E$ and momentum $p$
are related to the rest-mass $m$ of the particle by Einstein formula
$E^2/c^2-p^2=m^2c^2$. The wave function is spatially localized with finite-size
support which is decreasing as the rest-mass and/or group velocity are
increased. For a particle with vanishing rest-mass yet finite momentum, we show
that the group and phase velocities are equal to the velocity of light and the
wavelength is given by Einstein another formula $\lambda_P=h/p$.
