Wave-particle duality is a key part of quantum mechanics. All matter, which as you zoom in appears to be particulate, can also behave like waves. The wave properties of matter are not always noticeable. Scientists can directly observe the wave nature of atoms by cooling them down to near-absolute zero temperature. At these temperatures the wavelength of each particle is long and can overlap with other matter waves. Like water waves, atom-wave interference creates ripples and patterns. One of the neat aspects of this is that the interference is a single-particle effect--the atoms are not interacting.
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Ripples on a pond can overlap to form patterns having peaks and valleys. Similarly, the wave description of quantum mechanics allows atoms (and all quantum objects) to be in superposition states. It is this phenomenon of superposition states that, when applied to many qubits, is the basis for quantum computation and its extraordinary processing capabilities for certain tasks.