Electrons exhibit both wave-like and particle-like properties, known as wave-particle duality. While it is true that electrons can behave as waves, their wave-like nature alone does not explain how they repel each other.
Electron repulsion is primarily governed by the electromagnetic force, which arises due to the electric charge carried by electrons. Electrons possess a negative electric charge, and according to Coulomb's law, like charges repel each other.
When two electrons approach each other, their negatively charged fields interact. This interaction can be understood in terms of the exchange of virtual particles called photons, which are the carriers of the electromagnetic force. The exchange of photons between electrons creates a repulsive force that prevents the electrons from getting too close to each other.
Although the wave-like nature of electrons plays a role in their behavior and the distribution of their charge density, it does not directly explain the repulsion between them. The wave-like behavior of electrons is more apparent in phenomena such as interference and diffraction, where their wave nature becomes evident. However, the fundamental mechanism underlying their repulsion is the electromagnetic force resulting from their electric charges.