The objects you interact with every day are predictable – you can pick up a box, sit down in a chair without falling to the floor, or open a door without your hand passing through the knob. But if you zoom in on these objects all the way to the quantum level – where you look at the individual atoms – you’ll find that things start to behave somewhat strangely.

The typical size of quantum objects is a nanometer, or one-billionth of a meter. For scale, a human hair is 60,000-100,000 nanometers wide. At the nanoscale level, you cannot know where exactly a particle is in space – you can only calculate a probability of where it might be.

At the quantum level, particles exhibit wavelike behavior. Instead of discrete, tiny objects, particles act more like continuous waves. A particle’s properties, including properties as basic as its position in space, are defined in terms of probabilities. You can’t know exactly where the particle is, but you can estimate the chances of finding it within a certain region of space. You can compute these probabilities using Schrödinger’s equation, the solutions to which are called wave functions.

About a century ago in 1926, Austrian physicist Erwin Schrödinger developed the wave equation, which allowed him to calculate the probability that a particle exhibited a certain property from its wave functions.

Even though the human eye can’t parse what’s happening at the quantum scale, the way particles behave at that level influences how you experience the world. It gives plants their green color, provides the foundations for computer and information technology, and governs how many everyday materials........

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