Most recent TBTK release at the time of writing: v1.0.3<\/i>
\nUpdated to work with: v2.0.0<\/i><\/p>\n
One of the core strengths of TBTK<\/a> is the generality of the quantum systems that can be modeled and the ease with which such models can be created. In this post we will take a look at how the use of an IndexFilter can simplify this process further. In particular, we will show how to setup the Schr\u00f6dinger equation on a simple annulus shaped geometry and how to calculate the energy and probability density for a given state.<\/p>\n In addition to showing how to use an IndexFilter, this post also provides a simple example of quantum mechanics in polar coordinates. The solutions we arrive at show similarities with the s, p, and d orbitals, and the radial wave functions that appears as solutions to the Schr\u00f6dinger equation in a central potential (the Hydrogen atom). This without the need of introducing a spatially varying potential. As such it can give useful insights into aspects of quantum mechanics that can be difficult to grasp from the derivation of the solutions to the full fledged Schr\u00f6dinger equation in a central potential.<\/p>\n The material closely parallels the earlier post Direct access to wave function amplitudes and eigenvalues in TBTK<\/a>, which provide more details on some of the content that is treated more briefly here.<\/p>\n