On Robin boundary conditions and the Morse potential in quantum mechanics

The physical origin is investigated of Robin boundary conditions for wave functions at an infinite reflecting wall. We consider both Schr\"odinger and phase-space quantum mechanics (a.k.a. deformation quantization), for this simple example of a contact interaction. A non-relativistic particle moving freely on the half-line is treated as moving on the full line in the presence of an infinite potential wall, realized as a limit of a Morse potential. We show that the wave functions for the Morse states can become those for a free particle on the half-line with Robin boundary conditions. However, Dirichlet boundary conditions (standard walls) are obtained unless a mass-dependent fine tuning (to a reflection resonance) is imposed. This phenomenon was already observed for piece-wise flat potentials, so it is not removed by smoothing. We argue that it explains why standard quantum walls are standard. Next we consider the Wigner functions (the symbols of both diagonal and off-diagonal density operator elements) of phase-space quantum mechanics. Taking the (fine-tuned) limit, we show that our Wigner functions do reduce to the expected ones on the half-line. This confirms that the Wigner transform should indeed be unmodified for this contact interaction.Comment: 19 page

Fiber optic wavelength division multiplexing: Principles and applications in telecommunications and spectroscopy

Design and fabrication tradeoffs of wavelength division multiplexers are discussed and performance parameters are given. The same multiplexer construction based on prism gratings has been used in spectroscopic applications, in the wavelength region from 450 to 1600 nm. For shorter wavelengths down to 200 nm, a similar instrument based on longer fibers (500 to 1000 micrometer) has been constructed and tested with both a fiber array and a photodiode detector array at the output

Quirk shame

Although music historians have begun to consider some of the broad implications of large-scale digitization, the shift from traditional library- or archive-based methods of research to speculative Internet text searching remains largely invisible within an unchanged scholarly apparatus of footnotes and bibliographies. As a result, quirky details become easier to find, yet that ease is itself concealed, perhaps, this article argues, because to admit it might occasion a variety of academic shame. Fall 201

Using visualization for visualization : an ecological interface design approach to inputting data

Visualization is experiencing growing use by a diverse community, with continuing improvements in the availability and usability of systems. In spite of these developments the problem of how first to get the data in has received scant attention: the established approach of pre-defined readers and programming aids has changed little in the last two decades. This paper proposes a novel way of inputting data for scientific visualization that employs rapid interaction and visual feedback in order to understand how the data is stored. The approach draws on ideas from the discipline of ecological interface design to extract and control important parameters describing the data, at the same time harnessing our innate human ability to recognize patterns. Crucially, the emphasis is on file format discovery rather than file format description, so the method can therefore still work when nothing is known initially of how the file was originally written, as is often the case with legacy binary data. © 2013 Elsevier Ltd

Providing structural modules with self-integrity monitoring

With the advent of complex space structures (i.e., U.S. Space Station), the need for methods for remotely detecting structural damage will become greater. Some of these structures will have hundreds of individual structural elements (i.e., strut members). Should some of them become damaged, it could be virtually impossible to detect it using visual or similar inspection techniques. The damage of only a few individual members may or may not be a serious problem. However, should a significant number of the members be damaged, a significant problem could be created. The implementation of an appropriate remote damage detection scheme would greatly reduce the likelihood of a serious problem related to structural damage ever occurring. This report presents the results of the research conducted on remote structural damage detection approaches and the related mathematical algorithms. The research was conducted for the Small Business Innovation and Research (SBIR) Phase 2 National Aeronautics and Space Administration (NASA) Contract NAS7-961