Quantum matrix diagonalization visualized: https://arxiv.org/abs/1905.13269
We show how to visualize the process of diagonalizing the Hamiltonian matrix to find the energy eigenvalues and eigenvectors of a generic one-dimensional quantum system. Starting in the familiar sine-wave basis of an embedding infinite square well, we display the Hamiltonian matrix graphically with the basis functions alongside. Each step in the diagonalization process consists of selecting a nonzero off-diagonal matrix element, then rotating the two corresponding basis vectors in their own subspace until this element is zero. We provide Mathematica code to display the effects of these rotations on both the matrix and the basis functions. As an electronic supplement we also provide a JavaScript web app to interactively carry out this process.
6 pages, 2 figures. Submitted to the American Journal of Physics
A Do-it-yourself Spectrograph Kit for Educational Outreach in Optics and Photonics: https://arxiv.org/abs/1905.13242
We designed and built a do-it-yourself spectrograph assembly to demonstrate the concept of spectroscopy, an indispensable tool for exploring the cosmos. This spectrograph is designed for optical band (400-750 nm). It uses a transmission grating to disperse the light and a webcam to measure the spectrum. This spectrograph provides a resolving power (λ/δλ) of about 1000. This demonstration involves off-the-shelf materials costing less than $500, thus making it an easy to build demonstration kit for a school or public setting. The kit is well-suited for performing various science experiments and acquiring hands-on experience for students to learn the concepts such as coherence, spectral orders, resolving power, absorption and emission spectra. All of these concepts are an integral part of modern astronomical observations as well as various other fields in STEM such as biomedical engineering, chemical analysis, food and water quality, etc. This kit is portable and fully modular, making it apt for outreach purposes.
7 pages, 7 figures. Manuscript presented at SPIE Optics and Photonics 2018, San Diego, California