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arXiv quant-ph/0310159quant-phmath-phmath.MP
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本征函数沿直线定域的能量-动量算符

Energy-momentum operators with eigenfunctions localized along a line

Shaun N. Mosley

备注：
10 pages, errors corrected
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摘要：

动量算符$ {\bf p} = - i {\bx \nabla} $具有径向分量$ {\bf \tilde p} \equiv - i {\bf \hat{r}} ({1 \over r} \partial_r r).$我们证明了${\bf \tilde p} $是一个4-向量算符的空间部分，其零分量是一个正算符.它们的本征函数是沿着通过原点的轴局部化的。演化方程$ i \partial_t ψ= {\tilde p^0} ψ$的解是沿传播轴的波。这些波的洛伦兹变换产生像差和多普勒频移。我们简要地考虑自旋半和自旋一表示。

英文摘要：

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 ψ= {\tilde p^0} ψ$ 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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