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Spherium is the weird hypothetical stuff that forms when two electrons are confined to the surface of a sphere.

This substance is the brain child of Pierre-Francois Loos and Peter Gill at the Australian National University in Canberra, which they first revealed last year. Today, they continue their exploration of its properties and behaviour and turn up an interesting surprise.

Spherium, they say, is one of the few quantum systems for which it is possible to exactly solve the Schrodinger equation that describes its state for a certain part of the energy spectrum. But this is not the surprise.

Simple solvable models are of great interest to physicists because they can reveal important properties of a quantum system without the intractable mathematical complexity that usually arises. But the number of exactly solvable quantum systems can be counted on the fingers of one hand.

So in the last few years, quantum physicists have searched for so-called quasi-solvable models which can be exactly solved but only over a limited part of the energy spectrum. These turn out to be more numerous and so more useful. Developing them has turned into a quite an art.

Spherium falls into this category. And Loos and Gill do not mean any old sphere. They have worked out the properties of various d-dimensional spheres (a d-sphere is the surface of a d+1 dimensional ball).

The surprise is that electrons confined to the surface of a 3-sphere (ie to the surface of a 4-D ball) behave in a remarkably similar way to electrons confined to real 3D space. “We have therefore argued that 3-spherium may be the most appropriate model for studying “real” atomic or molecular systems,” says Loos and Gill.

They point, in particular, to the similarity between the properties of 3-spherium and helium ions. In some ways that’s not too hard to imagine. Clearly the hope is that spherium will help them understand other systems too.

That’s interesting and full of a certain kind of promise. What Loos and Gill seem to be hinting at is that the chemistry of spherium–the way it bonds together–will provide a new way to study the quantum behaviour of real molecules and artificial atoms.

And if it does, then who’s to say there isn’t a periodic table of spheres with 3, 4 and more electrons that might also yield quasi solvable results? Quantum chemistry might never be the same. I guess Loos and Gill will be working feverishly to let us know.

Ref: arxiv.org/abs/1004.3641: Excited States of Spherium

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