Comment on 'Overcoming misconceptions in quantum mechanics with the time evolution operator'

In their paper 'Overcoming misconceptions in quantum mechanics with the time evolution operator', Garcia Quijas and Arevalo Aguilar (2007 Eur. J. Phys. 28 147) examined the time-dependent wave function of a particle in the one-dimensional harmonic oscillator potential using two different methods. The two wave functions that the authors obtained through the methods have different analytical expressions. The authors showed numerically that the two wave functions lead to the same probability density. When the real parts of the wave functions are compared, however, they are different in their details. That was puzzling because both wave functions are supposed to be solutions of the same time-dependent Schrodinger equation with the same initial condition. We point out that the two wave functions are actually identical. We show this analytically.