Géza I. Márk
November 20, 1997
Research Institute for Materials Science,
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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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