Question

What are matter waves?

Answer 1

In order to answer this question, we will go through the whole concept of matter waves, as we know the matter wave is de-Broglie's hypothesis. And we will also mention the formula that shows the relation between wavelength and momentum.

Complete step-by-step solution:
Matter waves, which are an example of wave–particle duality, are an important aspect of quantum mechanics theory. All stuff behaves in a wavelike manner. A beam of electrons, for example, can be diffracted in the same way that a beam of light or a water wave may. However, in most circumstances, the wavelength is too short to have a practical effect on daily tasks.
In 1924, French scientist Louis de Broglie presented the idea that matter acts like a wave. The de Broglie theory is another name for it. De Broglie waves are the name given to matter waves.
The de Broglie wavelength, $\lambda$ is linked with a heavy particle (as opposed to a massless particle) and is connected to its momentum, $p$ , by the Planck constant, $h$ :
$\lambda = \dfrac{h}{p} = \dfrac{h}{{mv}}$
George Paget Thomson's thin metal diffraction experiment and the Davisson–Germer experiment, both involving electrons, were the first to reveal wave-like behaviour of matter, and it has since been proven for other elementary particles, neutral atoms, and even molecules.

Note: All matter, including the atoms that make up your body, has a wave-like character, which is known as de Broglie waves. The dual wave-particle duality of electrons is one of quantum physics' first and most fundamental discoveries.