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# Title: Sources of quantum waves

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.
 Comments: 12 pages, 7 inlined figures; typos corrected Subjects: Quantum Physics (quant-ph) Journal reference: J. Phys. A: Math. Gen. 34 (2001) 4289 DOI: 10.1088/0305-4470/34/20/303 Report number: EHU-FT/0007 Cite as: arXiv:quant-ph/0007066 (or arXiv:quant-ph/0007066v2 for this version)

## Submission history

From: Inigo L. Egusquiza [view email]
[v1] Wed, 19 Jul 2000 16:50:37 GMT (48kb)
[v2] Thu, 20 Jul 2000 11:07:59 GMT (48kb)