dorsal/arxiv
View SchemaThe vacuum electromagnetic fields and the Schrodinger picture
| Authors | A. J. Faria, H. M. Franca, G. G. Gomes, R. C. Sponchiado |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0510134 |
| URL | https://arxiv.org/abs/quant-ph/0510134 |
Abstract
Several authors have used the Heisenberg picture to show that the atomic transitions, the stability of the ground state and the position-momentum commutation relation [x,p]=ih, can only be explained by introducing radiation reaction and vacuum electromagnetic fluctuation forces. Here we consider the simple case of a nonrelativistic charged harmonic oscillator, in one dimension, to investigate how to take into account the radiation reaction and vacuum fluctuation forces within the Schrodinger picture. We consider the effects of both classical zero-point and thermal electromagnetic vacuum fields. We show that the zero-point electromagnetic fluctuations are dynamically related to the momentum operator p=-ih d/dx used in the Schrodinger picture. Consequently, the introduction of the zero-point electromagnetic fields in the vector potential A_x(t) used in the Schrodinger equation, generates ``double counting'', as was shown recently by A.J. Faria et al. (Physics Letters A 305 (2002) 322). We explain, in details, how to avoid the ``double counting'' by introducing only the radiation reaction and the thermal electromagnetic fields into the Schrodinger equation.
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"abstract": "Several authors have used the Heisenberg picture to show that the atomic\ntransitions, the stability of the ground state and the position-momentum\ncommutation relation [x,p]=ih, can only be explained by introducing radiation\nreaction and vacuum electromagnetic fluctuation forces. Here we consider the\nsimple case of a nonrelativistic charged harmonic oscillator, in one dimension,\nto investigate how to take into account the radiation reaction and vacuum\nfluctuation forces within the Schrodinger picture. We consider the effects of\nboth classical zero-point and thermal electromagnetic vacuum fields. We show\nthat the zero-point electromagnetic fluctuations are dynamically related to the\nmomentum operator p=-ih d/dx used in the Schrodinger picture. Consequently, the\nintroduction of the zero-point electromagnetic fields in the vector potential\nA_x(t) used in the Schrodinger equation, generates ``double counting\u0027\u0027, as was\nshown recently by A.J. Faria et al. (Physics Letters A 305 (2002) 322). We\nexplain, in details, how to avoid the ``double counting\u0027\u0027 by introducing only\nthe radiation reaction and the thermal electromagnetic fields into the\nSchrodinger equation.",
"arxiv_id": "quant-ph/0510134",
"authors": [
"A. J. Faria",
"H. M. Franca",
"G. G. Gomes",
"R. C. Sponchiado"
],
"categories": [
"quant-ph"
],
"title": "The vacuum electromagnetic fields and the Schrodinger picture",
"url": "https://arxiv.org/abs/quant-ph/0510134"
},
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