The discussion in Section 39.5 shows that the wave function = e-iwt is a stationary state, where

The discussion in Section 39.5 shows that the wave function ψ = ψe-iwt is a stationary state, where ψ is time independent and w is a real (not complex) constant. Consider the wave function ψ = ψ1e-iwt + ψ2ε-iw2t, where ψ1 and ψ2 are different time independent functions and w1, and w2 are different real constants. Assume that ψ1 and ψ2 are real-valued functions, so that ψ1* = ψ1, and ψ2* = ψ2. Is this ψ' a wave function for a stationary state? Why or why not?