I'm teaching basic chemistry and got a question that I found very interesting. All text books we use depict hydrogenic p-orbitals (or spherical harmonics) by first making a linear combination of p+ and p- wave functions in order to get real orthogonal px, py, pz. But the thing that should be of (primary)interest is the probability density of the orbitals. i.e. the orbiltal wave function times its complex conjugate. Taking this of the p+ or p- wave functions result in doughnut shaped probability densities (allowing for a particle analogy with non-zero angular momentum, i.e. the Bohr orbit).(adsbygoogle = window.adsbygoogle || []).push({});

The question was:

Is the traditional vizualization of the p-orbitals just made in order to be able to depict a real wave function?

My extension of the question is:

Can another linear combination be found that results in 3 orthogonal wave functions whose probability densities are e.g. elongated doughnuts with identical shapes (ellipsoids)? Could anyone give me an example of such a linear combination? I simply do not have the maths required.

This would be a nice tramsition from the particle view to the wave view and show that the old atomic symbol of three crossed ellipses is not so crazy after all.

Respectfully

Peter S

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# Alternative linear comb. to vizualize hydrogenic orbitals p,d etc

Can you offer guidance or do you also need help?

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