The question title kind of speaks for itself really. I was thinking of maybe using the orthogonality relation to try to show this: $$\int\_{-\infty}^{\infty}\phi\_n(x)\phi\_m(x)dx=\delta\_{nm}.$$ Alternatively, maybe since a stationary wavefunction is given by $$\phi(x)=A\sin{\frac{n\pi x}{L}}$$ it follows that it can be a superposition of two wavefunctions, and the new one would just have a different constant $A$ at the beginning. This sounds like a reasonable explanation so may well work, but does the statement **different energies** have any major significance?