November 20, 1997
Research Institute for Materials Science,
H-1525
Budapest,
P.O.Box 49,
Hungary
Tel.: +36-1-3959220
Fax: +36-1-3959284
E-mail: mark@sunserv.kfki.hu
An analysis of the behaviour of different wave packets is given
in one dimensional free space.
Several typical wave packet shapes are investigated:
Gaussian, Dirac delta, plane wave and different compact
supported ones.
Cases of jumps in the wave function, jumps in its
derivative and the infinitely smooth case (all derivatives are
continuous) are analysed.
The spectral properties and the decay form of the momentum space
wave function depend on the continuity properties of the wave packet
in coordinate space.
The initial shape of the wave packet determines its time development.
In non-relativistic quantum mechanics all wave packets with
bounded support spread to the whole space infinitely fast.
It is shown that while the Gaussian minimises the
Heisenberg uncertainty relation,
for our other wave packets
.
The time dependence of
is described by a simple
formula universal in the sense that
the value of the spreading speed depends
on the specific wave function shape only through
the value of 
.
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