Anisotropic Quantum Harmonic Oscillator

thingiverse

This piece embodies both physical representation and an exploration of human knowledge's extent and limitations. Quantum Mechanics (QM), the branch of physics explaining how particles behave at very small scales, forms the foundation of our current understanding of the Universe's workings. QM is the most successful theory in human history, having passed every experimental test with incredible precision. Without it, we wouldn't have laptops, smartphones, MRI machines, microprocessors, or lasers. Most material properties, like electrical conductivity or magnetism, are a direct result of QM. Some experimental values have been determined to an uncertainty of just a few parts per trillion. However, we can never predict for certain where even a single particle will be now or in the future. According to QM, particles don't have definite positions but are described by a wavefunction, which assigns a complex number to every point across space and time. While not being observed, the wavefunction changes in a completely known and deterministic way as described by the time-dependent Schrödinger equation. The motion is very similar to waves we're familiar with and understand like ripples on a lake's surface that can interfere with each other. But there's an inherent paradox in our understanding of the laws governing the Universe. Despite knowing everything about the wavefunction and its evolution in time being completely deterministic, solutions only give probabilities for finding a particle at any particular location if we choose to look. Once we actually make a measurement, we're unsure of the outcome; all we can be sure of are the a priori chances for each. This piece shows the probability density's evolution over time for a specific case: a particle rolling in an oval bowl, also known as an anisotropic 2D harmonic oscillator. The height of each figure represents the probability density – the chance that the particle will be found at that x and y position – for a single moment in time. This particle will slosh around the bowl in a state of indeterminate bliss until someone peers in, at which point it will snap into a particular definite position.