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Quantum Analogs

Physics students studying the Schrödinger Equation sometimes get lost in the land of partial differential equations, and even if they return safely, they might not have developed any physical intuition about the systems and solutions they’ve encountered. This Immersion is intended to show how such intuition and familiarity can be taught, via a powerful mathematical analogy between Schrödinger-Equation eigenstates on the one hand, and, on the other, the resonant modes of sound waves in air inside confined structures.

Photo of Quantum Analogs apparatus

The TeachSpin ‘Quantum Analogs’ experiment is particularly useful in teaching students about the emergence of spherical harmonics (in spherically-symmetric situations) and of band structure (in spatially-periodic situations). Participants can see not just the frequency spectrum of resonant modes inside a sphere, but also map out the angular structure of each such mode — the spherical harmonics can be encountered experimentally. Participants will also learn just what independent variables control the location and width in frequency of a band of states, and the number of states in a band.

The apparatus can be introduced using an ordinary electronic signal generator and oscilloscope, but it can also be driven and diagnosed using the ‘sound cards’ present in many personal-computer systems. Participants will gain confidence and familiarity with both methods, and will further profit from using the special software written for pc’s by Dr. Rene Matzdorf – a physics theorist who developed this experimental apparatus for his own students’ benefit.

Participants may optionally bring a laptop computer (especially one with internal sound cards, and external 3.5-mm input/output jacks); other hardware and software will be provided. Assuming the availability of ordinary lab tools and an adequate computer, this Immersion can be replicated for about $4500.