Yes, according to quantum mechanics, matter can exhibit both wave-like and particle-like properties simultaneously. This is known as wave-particle duality. It means that elementary particles, such as electrons, photons, and even larger particles like atoms and molecules, can exhibit behaviors characteristic of both waves and particles.
The double-slit experiment is a classic example that demonstrates this duality. When particles, such as electrons or photons, are fired one by one at a barrier with two slits, they can create an interference pattern on a screen behind the barrier, similar to what would be expected from waves. This suggests that the particles are behaving as waves, interfering with themselves as they pass through both slits.
However, when detectors are placed to determine which slit a particle passes through, the interference pattern disappears. The act of measuring the particle's position collapses its wave-like behavior, and it starts behaving more like a particle. This indicates that the particle's wave-like behavior is disrupted when its position is known with certainty.
Wave-particle duality is a fundamental concept in quantum mechanics and is supported by numerous experimental observations. It highlights the non-intuitive nature of quantum physics, where particles can exhibit behaviors that seem contradictory from a classical perspective.