<p><strong>Disclaimer:</strong> I am not a professional 3D printer, so I'm not really familiar with how 3D printing works.</p>

<p>I was thinking about trying to make a real life model of the atomic orbitals, to clearly see how the orbitals are really shaped. I thought about trying to 3D print a block, made up of colored transparent "ink", in such a way that the darkness of the color at a point in the block should be proportional to the ψ<sup>2</sup> value (probability of the electron cloud). This would print a block in which high density areas are darker than light intensity areas.</p>

<p>My question is, would it be possible to design an algorithm to print a specific darkness of ink at a specific location based on the computed value of ψ<sup>2</sup>, which is obtained by solving Schrödinger's Equation. Also, would it be possible to have this fullfilled at a reasonable price to be afforded by a regular customer, such as an engineering employee?</p>

problem definition
I'm not quite sure if it's really question for this group. Looks like the problem itself is more for programming or physics group. Having requested calculations (electron cloud shape) resolved, there will be something to print but...
printing probability cloud
at first, please take a look for example
here
it's a review of 3d printing technologies. i think you should have clear picture if your idea is feasible or not.
IMO it's not with todays technologies. in general (and deadly simlified) we have 3 main printing technics
out of solid (or semi-solid) filaments - can be colorful and semi-transparent but it's not homogenous in terms of your needs
out of solid powders - can be colorful but it cannot be transparent
out of liquids - can be really transparent and color but unfortunately not colorful
i'd say rendering but not printing is what you really need