Quantum dynamics means studying the evolution of an initially prescribed wave function. This is
analytically tractable for special wavefunctions for the simplest of the situations—free particle
and simple harmonic oscillator. The purely anharmonic oscillators are virtually impossible to
handle. We show here that the study of Ehrenfest’s equation provides an alternative route to
studying quantum dynamics. It does not give exact answers but clarifies some basic aspects of
quantum dynamics by providing a prescription for constructing equivalent simple harmonic
oscillators.