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The Schr\"{o}dinger equation of a charged particle in a uniform electricfield can be specified in either a time-independent or a time-dependent gauge.The wave-function solutions in these two gauges are related by a phase-factorreflecting the gauge symmetry of the problem. In this article we show that theeffect of such a gauge transformation connecting the two wave-functions can bemimicked by the effect of two successive extended Galilean transformationsconnecting the two wave-function. An extended Galilean transformation connectstwo reference frames out of which one is accelerating with respect to theother.

Gauge transformation through an accelerated frame of reference