This reminds me of a device by Sandia National Labs of a micro-electromechanical steam engine. Sandia's device uses resistive heating to vapourise the water and capillary forces retract the piston.
Anyone in-the-know care to comment on the relative merits and the relative scales?

Add in shaking, and you're essentially describing simulated annealing.
Without the shaking, you'll quickly converge to a local minimum. With shaking, you explore the possibilities nearby and, provided you shake it just right, you eventually converge on the global minimum.
Simulated annealing is a really common approach when you have lots and lots of variables; in this example, the free parameters are the locations of each of the spheres. The authors even use this in their paper as a check.

I actually have it patented. :)
(WO2006134552) FLEXIBLE DISPLAYS AND USER INPUT MEANS THEREFOR.
(Although I think Philips let the patent lapse, and I think they stopped doing anything about it years ago.)

We're both loosing and gaining it here on earth, and it's not really practicable to make it. :)

'Green lasers' are typically diode-pumped solid state lasers with a frequency-doubling crystal. It's not easy to make green light directly.

Oh. So it is. Nevermind. :)

Cambridge Consultants demonstrated something similar a few years ago. It's called Sprint and there's a great big picture of it here.

Gunwharf Quays in Portsmouth, UK has been doing this since about 2008 (not that this makes it in any way ok).

Some blog
BBC News video

You bring the light from a pulsed laser to a very tight focus inside a photoresist -- the same type of chemical used in standard photolithography. When this photoresist absorbs light with a wavelength of, say, 400nm, it cross-links to become a fairly solid plastic. In normal photolith, you'd illuminate a controlled area with 400nm light.

In two-photon polymerisation, you start with light of, say, 800nm, and you rely on two photons being absorbed at the same time, which together have enough energy to do what a single 400nm photon could. The key here is that, since the probability of this two-photon process depends on the square of the intensity, rather than linearly as in the case of normal one-photon processes, then you can localise it much better: with a tight focus, the chance of polymerising a ~100nm region near the focus is pretty much unity, while the chance of polymerising something away from the focus is pretty much zero. You then move that spot around inside the a blob of photoresist on a microscope slide.

Have a look at Nanoscribe GmbH for a commercial device, with images of some things they've made.

I was going to reply point by point, but I really must do something else with my Sunday.

"I am not aware of any relativistic QM theory. In fact, I believe that to be one of the things most actively sought in modern physics."

General Relativity is the problem. Resolving Quantum Mechanics and Special Relativity (i.e. everything except gravity) has been done. It's called Quantum Field Theory. (Specifically Quantum Electrodynamics, or QED, for all things relating to the Coloumb force.) A lot has been done since the 1920s. I'd be surprised if you could get any useful molecular results from the Schrodinger equation.

`Particle in a box` is a toy problem, designed to introduce the student to the idea of boundary conditions. Imagine a guitar string, fixed at both ends, and that's your physical model. The `wave` isn't electromagnetic, gravitational or the like; it is a description of probability amplitudes, the square of which corresponds to probability (in the generally used interpretation).

The particle doesn't bounce off the walls. It is spread out, and doesn't rattle around like a classical ball. (If it did, you could measure the recoil as it hit the walls!)

As for quantisation emerging: the postulates do not include discrete eigenvalues. Read them again. Preferably from a better text book. It only emerges when you apply quantum mechanics to a a specific situation.

"...2+2=5..." The maths of QM isn't as hard as for number theory. And is certainly a lot more interesting.

"Physics courses in college take the same path." [They state unjustified assumptions.]

Have you taken one? Depending on the university, students are introduced the the subject in a bit of a rush, and only later (often in an optional course) come back to carefully examine the postulates.

Sure, assumptions are necessary to simulate a real situation (like a molecule). Maybe it's not a clean theory. Or maybe we just don't know how to frame the maths to do it efficiently on a computer. Eitehr way, just because we have to simplfy it for a specific situation does not render the whole approach invalid.

I stand by my comment that you know too little (you don't need years of study) to say it's wrong. As far as I can tell, it's not classical, so it doen't make sense/feel right, so you conclude it must be wrong. A lot of work has gone in to trying to reporoduce results with classical mechanics only, and we'd all embrace it, if only it would work.