5.4   Local waves for local particles


While you and Cormorant have been having fun calculating de Broglie wavelengths, Nefertiti has been thinking about a deeper question. At length she tells you what’s on her mind: “The odd thing about Louis’ model, you know, is that he derived it without ever answering one big question: if a particle can behave like a wave, what exactly is waving?  I mean, if it’s a wave on the ocean it’s the up and down motion of the water; in the case of light it’s an oscillating electromagnetic field. So what about a matter wave?

As soon as she’s said this, the atmosphere in the pub changes. The ghostly physicists who have hitherto been happily playing dominoes and looking down their noses at the ghostly chemists, start to become restless. There are occasional heated exchanges; they separate into small groups and there is much pointing of ghostly fingers at other groups. It feels like things might turn ugly. The problem is that this is a hard question and even now, nearly a century after Louis made his proposal, there’s a lot of disagreement over how to interpret those waves.

"And something else" continues Nefertiti, "we derived the de Broglie equation by supposing a correspondence with a light wave, so it would seem simply to relate to an analogous sinusoidal wave. The problem is that such a wave goes on for ever – so how might this relate to an electron that seems to be localised in an atom?"

"Good point", says Cormorant.

A Danish voice pipes up from among the now brawling ghostly physicists. "Perhaps you would be interested in one of the most famously wrong answers in the history of physics?" Time for Niels Bohr to step into the frame. 

His thought was that in the electric field associated with the positively charged nucleus, an electron wave might curve around to form a circular, standing wave around it. As Louis himself pointed out, such a stationary wave might somehow act as a guide, controlling the motion of an orbiting electron. The beauty of this would be that if we assume circular electron orbits and a fixed wavelength for an electron in atom, it follows naturally that a stable stationary wave could only be formed at a radius compatible with accommodating a whole number of wavelengths around the circumference of the orbit:

This interpretation seems pleasingly easy to understand and it even had success in predicting energy levels in a hydrogen atom that were consistent with atomic spectra. Unfortunately, that turned out to be just about all it could do. It couldn’t, for example, answer one of the big, nagging questions about atomic structure:  since we know there is an attractive force between the nucleus and an electron, why doesn’t the electron simply realise its desire and collapse into the nucleus? Nor could it explain the complexity of the emission spectra of atoms with more than one electron or shed light on the relationships between atoms of different elements that are revealed by the periodic table. 

So we’ll have no more to do with this model. Niels offers a half-hearted cheer. "I have had to learn to accept that celebrating the failure of this model has become a rite of passage for every student of physics. Ah well .....".  Instead, in our quest to find the true form of a matter wave, we’ll make use of all that hard work we did developing the wave equation and use that as a starting point. We’ll develop this radically different approach in the next chapter.