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A Galilean boost to a frame moving with a complex velocity transforms the Berry–Balazs Airy function solution of the time-dependent Schrodinger equation into a square-integrable wavepacket. This packet has fixed momentum and energy; it contracts as time increases to zero, and then spreads again. The Berry–Balazs solution is revealed as a limiting form of a well-behaved free particle wavepacket. The topic is suitable for graduate or advanced undergraduate quantum mechanics courses.
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John Lekner (2009) studied this question.
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