Understanding Orbital Wavefunctions in Quantum Mechanics

[Physics Newbie]

I have poor concepts in Orbitals, wavefunctions etc. What i know is that quantum mechanics(study of sub atomic particles) talks about probability.
What i understand is wavefunction means probability of finding an electron in space around a nucleus, correct me i am wrong.So when we say that this s orbital has +ve wave function does it means that there is +ve probability of finding an electron in that spherical space around the nucleus i.e yes electron can be found in that region, and s orbital with -ve wave function means zero probability of finding electron in that space and when two orbitals with opposite wave functions overlap, the region they overlap results in no electron density i.e no electron can be found in that region.
Is it so? or i am on the wrong path.

 

[Dr. Courtney]

The probability density is the square of the wave function.

 

[Physics Newbie]

The probability density is the square of the wave function.

Sir i have learned that wave function has no physical meaning its only its square that makes sense, why its square in particular and not a cube? How was so the concept of wavefuntion put forward?

 

[Physics Newbie]

The probability density is the square of the wave function.

Sir what is understood about this topic, is that correct?

 

[Dr. Courtney]

https://en.wikipedia.org/wiki/Wave_function