Energy-momentum operators with eigenfunctions localized along a line

Details Energy-momentum operators with eigenfunctions localized along a line Energy-momentum operators with eigenfunctions localized along a line

2003-10-26

arxiv.org/abs/quant-ph/0310159v3

Physics

Quantum Physics

10 pages, errors corrected

Scientific paper

The momentum operator $ {\bf p} = - i {\bx \nabla} $ has radial component $ {\bf \tilde p} \equiv - i {\bf \hat{r}} ({1 \over r} \partial_r r).$ We show that ${\bf \tilde p} $ is the space part of a 4-vector operator, the zero component of which is a positive operator. Their eigenfunctions are localized along an axis through the origin. The solutions of the evolution equation $ i \partial_t \psi = {\tilde p^0} \psi $ are waves along the propagation axis. Lorentz transformations of these waves yield the aberration and Doppler shift. We briefly consider spin-half and spin-one representations.

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