Louis de Broglie suggested that, if a particle like electron has momentum and wavelength associated with it (due to Planck's constant), then it might be a wave. The region where it exists are those where these waves interfere constructively. But these (electrons and protons) are the particles with mass and charge. Particles with which matter is made of. Matter which we can touch and feel and interact with on a macro level. How can matter thus exhibit a wave-like nature?
What is the nature of such a wave? (We consider it a wave just because the equation closely resembles a classical wave). Is it similar to the waves that occur in nature, or something entirely different?