The Importance of Boundary Conditions in Quantum Mechanics

Abstract

We discuss the role of boundary conditions in determining the physical content of the solutions of the Schrodinger equation. We study the standing-wave, the ``in,'' the ``out,'' and the purely outgoing boundary conditions. As well, we rephrase Feynman's $+i\epsilon$ prescription as a time-asymmetric, causal boundary condition, and discuss the connection of Feynman's $+i\epsilon$ 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.

Contribution to the proceedings of the ICTP conference "Irreversible Quantum Dynamics," Trieste, Italy, July 2002

References in corpus (4)

• A Pedestrian Introduction to Gamow Vectors
• Rigged Hilbert Space Treatment of Continuous Spectrum
• Rigged Hilbert Space Approach to the Schrodinger Equation
• Formal and Precise Derivation of the Green Functions for a Simple Potential

Cited by in corpus (2)

• On the inconsistency of the Bohm-Gadella theory with quantum mechanics
• Does consciousness really collapse the wave function? A possible objective biophysical resolution of the measurement problem