THE ANALYTICAL NON-SERIES TIME EVOLUTION SOLUTION OF ONE DIMENSIONAL OSCILLATOR SCHR?DINGER EQUATION
In 1926,E.Schrödinger found an analytical solution for the time evolution of the one-dimensional harmonic oscillator Schrödinger Equation.This solution is not in the form of a summation of energy eigenstate wave functions,which provides a new perspective on the time evolution in quantum mechanics.This paper mainly analyzes this analytical time evolu-tion solution and presents two derivation methods.Then the paper further generalizes to ob-tain more non-series analytical solutions for time evolution oscillator,and finds the recursive relation to obtain these analytical solutions.Finally,the educational significance and applica-tions of these analytical solutions are discussed.
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