Abstract: A generalized analysis for symmetry in quantum mechanics is presented. The associated conserved quantities are extended to time-dependent ones. It is shown that a single particle （including the relativistic case） moving in a static uniform magnetic field and a time-dependent linear potential possesses space translation invariance. The translated wave function and the time-dependent conserved quantities are obtained.

Key words: symmetry, time-dependent conserved quantity, space translation invariance, uniform external field