Abstract
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 Schrödinger equation. The effects of both zero-point and thermal classical electromagnetic vacuum fields, characteristic of stochastic electrodynamics, are separately considered. Our study confirms that the zero-point electromagnetic fluctuations are dynamically related to the momentum operator p=−i ℏ ∂/∂ x used in the Schrödinger equation.
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References
Dalibard, J., Dupont-Roc, J., Cohen-Tannoudji, C.: Vacuum fluctuations and radiation reaction: identification of their respective contributions. J. Phys. 43, 1617 (1982)
Dalibard, J., Dupont-Roc, J., Cohen-Tannoudji, C.: Dynamics of a small system coupled to a reservoir: reservoir fluctuations and self-reaction. J. Phys. 45, 637 (1984)
França, H.M., Franco, H., Malta, C.P.: A stochastic electrodynamics interpretation of spontaneous transitions in the hydrogen atom. Eur. J. Phys. 18, 343 (1997)
Marshall, T.W.: Random electrodynamics. Proc. Roy. Soc. Ser. A 276, 475 (1963)
Boyer, T.H.: General connection between random electrodynamics and quantum electrodynamics for free electromagnetic fields and for dipole oscillator systems. Phys. Rev. D 11, 809 (1975), see Sect. III-B for a justification of the use of the dipole approximation
de la Peña, L., Cetto, A.M.: The Quantum Dice. An Introduction to Stochastic Electrodynamics. Kluwer Academic, Dordrecht (1996)
Barone, P.M.V.B., Caldeira, A.O.: Quantum mechanics of radiation damping. Phys. Rev. A 43, 57 (1991)
Senitzky, I.R.: Dissipation in quantum mechanics. Phys. Rev. 119, 670 (1960)
Dechoum, K., França, H.M.: Non-Heisenberg states of the harmonic oscillator. Found. Phys. 25, 1599 (1995); Erratum 26, 1573 (1996)
Scully, M.O., Zubairy, M.S.: Quantum Optics. Cambridge University Press, Cambridge (1997), see Chap. 5
Husimi, K.: Miscellanea in elementary quantum mechanics, II. Prog. Theor. Phys. 9, 381 (1953)
Faria, A.J., França, H.M., Malta, C.P., Sponchiado, R.C.: Critical assessment of the Schrödinger picture of quantum mechanics. Phys. Lett. A 305, 322 (2002)
Sokolov, A.A,, Tumanov, V.S.: The uncertainty relation and fluctuation theory. Sov. Phys. JETP 3, 958 (1957)
Milonni, P.W.: The Quantum Vacuum: An Introduction to Quantum Electrodynamics. Academic Press, New York (1994), see Sect. 2.6
Faria, A.J., França, H.M., Sponchiado, R.C.: Tunneling as a classical escape rate induced by the vacuum zero-point radiation. Found. Phys. 36, 307 (2006)
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Faria, A.J., França, H.M., Gomes, G.G. et al. The Vacuum Electromagnetic Fields and the Schrödinger Equation. Found Phys 37, 1296–1305 (2007). https://doi.org/10.1007/s10701-007-9152-6
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DOI: https://doi.org/10.1007/s10701-007-9152-6