The Importance of Boundary Conditions in Quantum Mechanics

Details The Importance of Boundary Conditions in Quantum Mechanics The Importance of Boundary Conditions in Quantum Mechanics

2003-02-25

arxiv.org/abs/quant-ph/0302184v1

Lect.Notes Phys. 622 (2003) 327-339

Physics

Quantum Physics

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

Scientific paper

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.

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