Quantum Analogs is TeachSpin’s contribution to the teaching of wave mechanics. The tag line, “Acoustic Experiments Modeling Quantum Phenomena,” best sums up what these unique experiments are about. Anyone who has taught quantum mechanics knows how difficult it is for students to “wrap their heads around” the subtle predictions of this remarkable theory. The idea at the heart of this apparatus is the analogy between the mathematics of the Schrödinger wave equation, and the wave equations that describe the behavior of ordinary sound waves in air. The various parts of our acoustic apparatus will allow students to explore acoustic analogs to quantum-mechanical systems in one, and three, dimensions. One of the advantages of the ‘acoustic analog’ is that sound phenomena occur on a very human scale of length and time.

TeachSpin’s first international collaboration, Quantum Analogs was developed with Professor Rene Matzdorf of the University of Kassel. Although officially a “theorist”, Professor Matzdorf, as a true teacher, recognized that for many people, even theorists, the ability to manipulate concrete phenomena rather than just equations both enhances conceptual understanding and encourages exploration. Manipulating equations sequentially to see the effect of changing the location of a defect on the band gaps of a semiconductor is one thing. Being able to vary the location or shape of a physical object and observe the band-gap changes within moments, encourages a far wider range of experimentation and may even lead to a kind of “instinct” that is usually available only to those for whom equations have a life of their own.

Professor Matzdorf has created an extensive manual for the instrument. The manual begins with a mathematical analysis of the similarities between the equations for standing waves in a tube and the eigenstates of a particle in a box. Students can then proceed through a series of experiments in which the standing waves in spheres and segmented tubes become analogs for the hydrogen atom, the hydrogen molecule and semiconductors.

Initial explorations for each section of the experiment are done using a signal generator and oscilloscope. In addition, Professor Matzdorf has created software which allows students to use a computer to record up to four experimental spectra on the same screen. The effects of changes can be explored efficiently not only qualitatively but quantitatively as well. This software is free, but comes without any warranty or liability. For the users of this experiment, Professor Matzdorf has created a special web page which answers frequently asked questions and provides software updates. The page also offers several excellent visualization programs that users are welcome to download.