主题：【原创】关于粒子性和波动性 -- witten1

Re: What is the velocity of a relativistic electron?

On 2008-02-13, Juan R. Gonzàlez-lvarez <[email protected]> wrote:

> I find different answers:

>

> ((Classical electrodynamics))

>

> v < c

>

> ((Relativistic Quantum Mechanics))

>

> v = c using Dirac equation for |PSI>.

Eh, no.

You are confused by an archaic paradox. The paradox consists of identifying the operator c*alpha (in the usual 3+1 Dirac equationnotation) with the physical velocity, which quite obviously doesn't work. For a modern discussion of the Dirac electron's velocity operator,see [1] where the author discusses the Foldy-Wouthuysen transformation and how to use it to get the correct operator obeservable. See also [2]for some more discussion and references.

The velocity operator thus obtained, satisfies the Heisenberg equationsof motion v = dx/dt and the well known relation v = p/m in the non-relativistic limit. Note, here x is not the spatial argument of the usual Dirac wave function. It is also obtained through the Foldy-Wouthuysen transformation, or from the formula given by Newton andWigner (again, see [2]). Once a particular time axis has been chosen,this operator x is unique (up to translations of the origin ofcoordinates).