Anisotropic Quantum Harmonic Oscillator by lnemzer

Last crawled date: 3 years ago

This piece is simultaneously a physical representation of data, as well as an exploration of the extent and limitations of human knowledge. Quantum Mechanics (QM) the branch of physics that describes how particles act at very small scales, and is a fundamental part of our best understanding of how the Universe works. QM the most successful theory in Human history, having successfully passed, with an incredible degree of precision, every experimental test. Without it, we would not have laptops, smartphones, MRI machines, microprocessors, or lasers. Most properties of materials, like electrical conductivity or magnetism, are a direct result of QM, and some experimental values have been determined to uncertainty of a few parts per trillion. But amazingly, we can never predict for certain where even a single particle will be, now or in the future. According to QM, particles do not have definite positions, but rather are described by a wavefunction, that assigns a complex number to every point in space across the Cosmos. 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 are familiar with and understand like ripples on the surface of a lake that can interfere with each other.
But there is an inherent paradox in our understanding of the laws the govern our Universe. Despite the fact that we know everything there is to know about the wavefunction, and its evolution in time is completely deterministic, the solutions only give probabilities to find a particle in every particular location if we would choose to look. Once we actually make a measurement, we cannot be sure of the outcome, only the a priori chances for each. This piece shows the evolution of the probability density over time for a particular 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 that 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.