Question

Why we use boundary condition in quantum mechanics?

Answer 1

$\textsc{\Huge{\red{Boundary\:Condition}}}$

We discuss the role of boundary conditions in determining the physical content of the solutions of the Schrödinger equation. We study the standing-wave, the “in,” the “out,” and the purely outgoing boundary conditions. As well, we rephrase Feynman’s +iε prescription as a time-asymmetric, causal boundary condition, and discuss the connection of Feynman’s +iε 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.