A matter wave, also known as a de Broglie wave or a wave function, is different from classical waves such as electromagnetic waves or sound waves. It is associated with particles, such as electrons or other fundamental particles, and is described by quantum mechanics.
Matter waves are not classified as either transverse or longitudinal like classical waves. Instead, they are described by wave functions that represent the probability distribution of finding a particle at different positions or with different momenta.
The behavior of matter waves is typically represented by wave equations, such as the Schrödinger equation, which governs the evolution of the wave function. The solutions to these equations provide information about the particle's energy, momentum, and other properties.
It's important to note that matter waves do not have a direct physical analog in terms of the motion of matter in a medium like classical waves. They are a fundamental concept in quantum mechanics, describing the wave-particle duality of quantum particles.