Re: Electron's zitterbewegung

johndevers@xxxxxxxxxxxxxx wrote:
> Tony wrote:
> > I was reading Hestenes articles on electron ZBW and wonder if there are
> > any news on it, new progress or problems, or new experiments that may
> > or may not favor it?
>
> I came across this paper during my recent surfing.
>
> http://link.aps.org/abstract/PRL/v94/e206801
>
> Zitterbewegung of Electronic Wave Packets in III-V Zinc-Blende
> Semiconductor Quantum Wells
>
> We study the zitterbewegung of electronic wave packets in III-V
> zinc-blende semiconductor quantum wells due to spin-orbit coupling. Our
> results suggest a direct experimental proof of this fundamental effect,
> confirming a long-standing theoretical prediction. For electron motion
> in a harmonic quantum wire, we numerically and analytically find a
> resonance condition maximizing the zitterbewegung.

This is an interesting article. But I would hesitate relating their
findings to the zitterbewegung of a relativistic electron. What the
article finds is that a term in the Hamiltonian that couples a
particle's spin to its momentum (what they call a spin-orbit coupling
term) generically introduces an oscillating component to the motion of
the particle. The oscillation frequency is proportional to the
coupling constant in front of the spin-orbit interaction term.

This is not particularly surprising. Even writing down the classical
equations of motion with such a Hamiltonian, we get such an oscillating
component to the particle motion. In the Dirac equation, the situation
is somewhat different. For the free electron case, the zitterbewegung's
characteristic frequency is very high (on the order of the mass of the
electron, 0.5 MeV). It is very hard to observe an electron's motion
with high enough precision at a good enough time resolution. So even if
this effect was real, it would be really hard to see. Also, it can be
seen only for wave functions that contain both negative and positive
frequency Fourier modes. States described by such wave functions can be
thought of as superpositions of an electron and a positron. Such states
would have indefinite charge, which is unlike any particle that we've
observed to date. All particles that we've seen have had definite
electric charge. In other words, it is unlikely that a state that
exhibits zitterbewegung is physically realizable. And again, even if it
were, the effect would be very hard to see. That's why I doubt
zitterbewegung will ever be observed.

Once we are content with dealing only with either electron or only
positron states, the zitterbewegung puzzle goes away. However, to see
this a more careful treatment of the Dirac equation is required. One
can be found, for example, in

Paul Strange
_Relativistic quantum mechanics: with applications in condensed matter
and atomic physics_ (CUP, 1998)

Hope this helps.

Igor

.

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