dorsal/arxiv
View SchemaEnergy-momentum operators with eigenfunctions localized along a line
| Authors | Shaun N. Mosley |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0310159 |
| URL | https://arxiv.org/abs/quant-ph/0310159 |
Abstract
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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"abstract": "The momentum operator $ {\\bf p} = - i {\\bx \\nabla} $ has radial component $\n{\\bf \\tilde p} \\equiv - i {\\bf \\hat{r}} ({1 \\over r} \\partial_r r).$ We show\nthat ${\\bf \\tilde p} $ is the space part of a 4-vector operator, the zero\ncomponent of which is a positive operator. Their eigenfunctions are localized\nalong an axis through the origin. The solutions of the evolution equation $ i\n\\partial_t \\psi = {\\tilde p^0} \\psi $ are waves along the propagation axis.\nLorentz transformations of these waves yield the aberration and Doppler shift.\nWe briefly consider spin-half and spin-one representations.",
"arxiv_id": "quant-ph/0310159",
"authors": [
"Shaun N. Mosley"
],
"categories": [
"quant-ph",
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"title": "Energy-momentum operators with eigenfunctions localized along a line",
"url": "https://arxiv.org/abs/quant-ph/0310159"
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