Abstract. We discuss the role of boundary conditions in determining the physical content of the solutions of the Schr\"odinger equation. We study the standing-wave, the in,'' the out,'' and the purely outgoing boundary conditions. As well, we rephrase Feynman's $+i \varepsilon$ prescription as a time-asymmetric, causal boundary condition, and discuss the connection of Feynman's $+i \varepsilon$ prescription with the arrow of time of Quantum Electrodynamics. A parallel of this arrow of time with that of Classical Electrodynamics is made. We conclude that in general, the time evolution of a closed quantum system has indeed an arrow of time built into the propagators.