Classical physics is built around a comforting promise: give it enough information about a system right now, and it will tell you exactly where everything will be later. Quantum mechanics abandons that promise entirely for particles at very small scales. The Schrödinger equation, the central equation governing how quantum systems evolve, doesn't output a definite position or velocity at all. It outputs a wavefunction — a mathematical description of probability — and according to the standard interpretation of quantum mechanics, that probability isn't a stand-in for hidden information we simply haven't measured yet. It may be all there genuinely is.
A wave that spreads possibility, not certainty
The wavefunction the Schrödinger equation describes evolves smoothly and deterministically over time, much like a classical wave — but what it represents is fundamentally different from a wave of water or sound. Squaring the wavefunction's value at a given location gives the probability of finding the particle there if you were to measure its position, which means the particle doesn't have one definite location before measurement in the way classical intuition assumes. Instead, it exists in a genuine superposition of possible locations, weighted by that probability distribution, until an act of measurement forces a single, definite outcome — a transition physicists call wavefunction collapse, and one the Schrödinger equation itself doesn't describe or explain, only sets up the probabilities for.
Predictable statistics from an unpredictable individual event
This might sound like it makes quantum mechanics an unreliable, unpredictable theory, but the opposite is true in a specific, important sense: while you can't predict where any single particle will be found on any single measurement, the Schrödinger equation predicts the probability distribution across many repeated measurements with extraordinary precision, confirmed experimentally across an enormous range of systems. The unpredictability lives at the level of the individual event; the statistics governing the aggregate are as precisely predictable as anything in classical physics, which is exactly the strange combination — deterministic evolution of pure probability, genuine randomness at the moment of measurement — that makes quantum mechanics feel so different from the physics that came before it.
What we're still unsure about
The Schrödinger equation's mathematical predictions have been confirmed to extraordinary precision across decades of experiments, and there's no scientific dispute about its practical accuracy. What remains genuinely unresolved, even among physicists who agree entirely on the mathematics, is what's actually happening during "wavefunction collapse" and what the wavefunction itself really represents — competing interpretations of quantum mechanics (Copenhagen, many-worlds, pilot-wave theories, and others) all reproduce the same experimentally verified predictions while disagreeing sharply on the underlying physical or philosophical picture, and there's currently no experiment known that can distinguish decisively between them.
This sits inside Quantum Mechanics & the Schrödinger Equation, one of seven topics in Modern Physics, one of five domains in Physics, one of seventeen subjects the app can quiz you on.