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Sources of quantum waves

A. D. Baute·I. L. Egusquiza·J. G. Muga
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Abstract

Due to the space and time dependence of the wave function in the time dependent Schroedinger equation, different boundary conditions are possible. The equation is usually solved as an ``initial value problem'', by fixing the value of the wave function in all space at a given instant. We compare this standard approach to "source boundary conditions'' that fix the wave at all times in a given region, in particular at a point in one dimension. In contrast to the well-known physical interpretation of the initial-value-problem approach, the interpretation of the source approach has remained unclear, since it introduces negative energy components, even for ``free motion'', and a time-dependent norm. This work provides physical meaning to the source method by finding the link with equivalent initial value problems.

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A. D. Baute, I. L. Egusquiza, J. G. Muga. 2000-07-20. Sources of quantum waves. https://doi.org/10.1088/0305-4470%2F34%2F20%2F303

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