What do the positive and negative signs on the atomic orbitals diagram imply? [closed]








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I was reading up on wave functions and electrons behaving like a wave when they are bound in an atom. In the orbital diagram, the + and - signs don't make any sense to me, and the reasoning that one side of the nucleus taken as positive displacement is probably wrong. Can someone explain it?




The sign on [atomic orbital](https://en.wikipedia.org/wiki/Atomic_orbital) diagram represents the sign of the respective [wave function,](https://en.wikipedia.org/wiki/Wave_function) (a solution of the [Schroedinger equation](https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation)). It is analogical to sign of sin(x) function with positive and negative sections.


There are 2 major implications:


* For adjacent atoms, overlapping of orbital parts with the same/opposite sign causes constructive/destructive wave interference, known from classical physics. 2 electrons with the same quantum numbers in the same atom would lead to their wave function mutual cancellation and zero probability.
* Regions of the given orbital with the opposite signs are separated by 3D "node surfaces" with $|\Psi|^2=0$ and zero probability density of electron occurrence.


An orbital with the main quantum number n has n-1 of such node surfaces. E.g. the orbital 3s contains 2 inner spherical 3D surfaces with zero probability of the electron occurance, having 3 radial probability maxima.


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