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Can someone explain why electrons move from high to low potential regions in quantum mechanics? By the way, what is the very definition of this potential? Moreover, how does this generalize to other particles?

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    $\begingroup$ We don't need quantum mechanics and the relation is perfectly general: $\vec{F}=-\vec{\nabla}V$ $\endgroup$ – Danu May 2 '14 at 12:45
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First of all, before anyone gets mad: We do not know. You could say that it just turned out that way, but in nature things tend toward their minimum states of energy. You simply have to accept this axiom(think about particle excitement and the ground state). For a charged particle the Potential energy equation is:

$U_{potential}=\cfrac{(k*q*Q)}{R}$,

Where $k$ is Coulomb's constant, and $r$ is the distance between the charges.

So, because the electron's charge is negative, a greater distance would yield a larger potential energy value. Since we said that in nature, particles tend toward their lowest states of energy (once again think of gamma decay, or something of the sort), it would make no sense for an electron to travel away from a region that causes it to have lower energy state. Consequently, electrons move toward the region of a lower state of energy.

$\textbf{Your next question should be: Why do thing tend toward their lowest states of energy?}$

I will attempt to answer this as well:

It has to do with the principle of $\textit{minimum total potential energy}$, a concept that denotes the phenomenon that, innately, structures in nature will tend towards their lowest states of potential energy.

The reasoning for this is intuitive if one considers the second law of thermodynamics, which states that in nature, a bodies will tend toward their equilibrium, where entropy is at a maximum. Simply put: if something is cold it is in a state of $\textbf{low entropy}$, and if something is hot is in a in a state of $\textbf{high entropy}$.

Consequently, if something has a higher heat content, it has a lower potential energy, and since things tend toward maximum entropy, we can reason that things tend toward low energies as well. For example, an electron and a proton will combine to form a neutral hydrogen atom, which has less charge than the individual particles (even if they are infinitely far away). So, if this applies even at infinite distances, then every particle is connected in this way, and they will all tend toward their lowest states of energy.

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