Problem 2.17 – Griffith’s Intro to QM

Problem 2.17

Show that $\left[ Ae^{ikx}+Be^{-ikx}\right]$ and $\left[C\cos{kx}+D\sin{kx}\right]$ are equivalent ways of writing the same function of $x,$ and determine the constants $C$ and $D$ in terms of $A$ and $B,$ and vice versa. Comment: In quantum mechanics, when $V=0,$ the exponentials represent traveling waves, and are most convenient in discussing the free particle, whereas sines and cosines correspond to standing waves, which arise naturally in the case of the infinite square well.