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It is shown that if a complete set of mutually commuting operators is formedby constants of motion, then, up to a factor that only depends on the time,each common eigenfunction of such operators is a solution of the Schr\"odingerequation. In particular, the operators representing the initial values of theCartesian coordinates of a particle are constants of motion that commute witheach other and from their common eigenfunction one readily obtains the Greenfunction.

Solution of the Schr\"odinger equation making use of time-dependent constants of motion