What are matter waves and how do they behave in the context of quantum mechanics?

Matter waves are a concept in quantum mechanics that describe the wave-like behavior of particles, such as electrons and atoms. These waves represent the probability of finding a particle at a certain position. In quantum mechanics, matter waves exhibit properties of both particles and waves, such as interference and diffraction. This duality is a fundamental aspect of quantum theory and is essential for understanding the behavior of particles at the atomic and subatomic levels.