THE ANALYTICAL NON-SERIES TIME EVOLUTION SOLUTION OF ONE DIMENSIONAL OSCILLATOR SCHRÖDINGER 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 evolution solution and presents two derivation methods. Then the paper further generalizes to obtain more non-series analytical solutions for time evolution oscillator, and finds the recursive relation to obtain these analytical solutions. Finally, the educational significance and applications of these analytical solutions are discussed.