Significance of wave function and its sign

[vaibhavsharma]

I have three question regarding the electronic wavefunction $$\Psi$$

Ques 1 What does value of wavefunction of any orbital signify ? Is it just a mode of calculating
other quantities like probability amplitude etc. or does it have a significance in itself ?

Ques 2 What does the radial part of wave function of any orbital represent for that orbital ?

Ques 3 What is significance of positive and negative phases of a wavefunction of any orbital ?
I know that when orbitals' wavefunction combine out of phase they form anti-bonding
and when they combine in phase they form bonding orbitals but is there individual
importance of these phases for that orbital ?

 

[alxm]

Ques 1 What does value of wavefunction of any orbital signify ? Is it just a mode of calculating other quantities like probability amplitude etc. or does it have a significance in itself ?

It's not known what, if anything, the wave function actually signifies in itself. So it's an acceptable stance (but not the only one) to simply view it as a tool to calculate the directly-observable quantities.

What is significance of positive and negative phases of a wavefunction of any orbital ?

The signs and phases cause interference (as with classical waves) which end up changing the overall probabilities (as in the double-slit experiment, for instance). So the respective phases of the wave functions of two interacting particles is important and leads to measurable differences, but changing the global phase and sign doesn't change anything.

Ques 2 What does the radial part of wave function of any orbital represent for that orbital ?

Well any wave function represents the location probability distribution of a particle (as the magnitude of the wave function) and the momentum of the particle (as the derivative of the wave function, a thus a 'sharper' wave function means higher momentum). So if you consider this in a spherical coordinate system, then the radial wave function is the radial probability distribution, and its derivative a measure of the linear momentum.

 

[soothsayer]

The wave function is really just a way to model the wave-like nature of particles, but as the wave function is a complex function, there isn't any concrete physical reality to it.

 

[vaibhavsharma]

thanx for help...
One more question
In many books i have seen that while describing the $$\Psi$$ vs radial distance 'r' graph of any orbital ,it is shown in two ways.For example 1s orbital - in one way they write it such that whole graph is in +ve phase [y = e^-x graph] whereas in other way the image of graph is taken along x-axis such that whole of the graph is in -ve phase [ y = -(e^-x)].Generally for any orbital the second graph is the 'image of first graph along x-axis.After that they use it in concept of "combination of wavefunctions of orbitals"(molecular orbitals) by saying that combination of that whole +ve graph with another +ve graph(or combination of -ve graph with -ve graph) is 'in phase' combination and yields 'bonding molecular orbital' and combination of +ve with -ve is 'out phase' combination yielding anti-bonding orbital.
The question is- "Do the orbitals actually exist in both ways and what is the significance of taking the image about x-axis always"?