04-170 R. de la Madrid

The Importance of Boundary Conditions in Quantum Mechanics (102K, Gzipeed tar file) May 31, 04

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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.

Files: 04-170.src( 04-170.keywords , physprbb.sty , sprmindx.sty , author.tex , cropmark.sty , subeqnar.sty , svmult.cls )