I recently came across Molecular Orbital Theory. In this, if two electrons are bonding, their waves merge and they form a proper bond. But this is directly opposite to the particle theory, according to which they should repel each other as they have like charges.
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Take a nice simple system like a hydrogen molecule. It's true that the two electrons repel each other, but at the same time they are attracted by the positive charge of the two protons.
If we start with an $\ce{H2+}$ ion, with just a single electron, it should be obvious that the electron is tightly bound because it feels an attractive force from both the protons.
Now imagine adding the second electron to form a neutral hydrogen molecule. The second electron will be repelled by the first electron that is already present but it will be attracted by both the protons, and the attraction from the two protons wins. The binding energy of the second electron in a hydrogen molecule is about 15.4 eV, so it is even more strongly bound than the electron in a hydrogen atom.
Note that this is not related to the wave/particle duality. Wave particle duality is in any case a misguided concept since particles are quantum fields not waves or particles – they simply behave approximately like waves in some circumstances and approximately like particles in others. See this post on the Physics Stack Exchange for more on this.
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$\begingroup$ For some quantitative analysis, see this question & my answer. $\endgroup$– TAR86Commented Nov 5, 2017 at 12:37
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$\begingroup$ I would add the influence of the Pauli exclusion principle. $\endgroup$– VerktajCommented Nov 5, 2017 at 21:54