Critical assessment of the Schrödinger picture of quantum mechanics

Faria, A. J. de; França, Humberto de Menezes; Malta, C. P.; Sponchiado, R. C.

doi:10.1016/s0375-9601(02)01508-6

Cited by 9 publications

(28 citation statements)

References 19 publications

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“…This result is in semi-quantitative agreement with our classical stochastic calculation based on the Kramers theory with zero-point radiation. Finally, we would like to say that the direct inclusion of zero-point and thermal fluctuations into the Schrödinger equation (19) is a very delicate problem that is out of the scope of the present work.…”

Section: Comparison With Experimental Data and Conclusionmentioning

confidence: 99%

Tunneling as a Classical Escape Rate Induced by the Vacuum Zero-point Radiation

2006

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We make a brief review of the Kramers escape rate theory for the probabilistic motion of a particle in a potential well U(x), and under the influence of classical fluctuation forces. The Kramers theory is extended in order to take into account the action of the thermal and zero-point random electromagnetic fields on a charged particle. The result is physically relevant because we get a non-null escape rate over the potential barrier at low temperatures (T → 0). It is found that, even if the mean energy is much smaller than the barrier height, the classical particle can escape from the potential well due to the action of the zero-point fluctuating fields. These stochastic effects can be used to give a classical interpretation to some quantum tunneling phenomena. Relevant experimental data are used to illustrate the theoretical results.

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Section: Comparison With Experimental Data and Conclusionmentioning

confidence: 99%

Tunneling as a Classical Escape Rate Induced by the Vacuum Zero-point Radiation

2006

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“…In this way, we have shown that the main conclusion of [2] is incorrect. Of course, the general arguments against the Schrödinger picture [1] mentioned in the introductory paragraph are not discredited by our result.…”

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confidence: 78%

“…The explicit value of the right-hand side of (1) is given by (14') (where the prime denotes equations in [2]). In the Schrödinger picture, they show that the ground-state wave function takes the form…”

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confidence: 99%

Comment on: “Critical assessment of the Schrödinger picture of quantum mechanics”

Nikolić

2004

Physics Letters A

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Recently, Faria et al [Phys. Lett. A 305 (2002) 322] discussed an example in which the Heisenberg and the Schrödinger pictures of quantum mechanics gave different results. We identify the mistake in their reasoning and conclude that the example they discussed does not support the inequivalence of these two pictures.PACS: 03.65.Ta Keywords: Foundations of quantum mechanics A long time ago, Dirac argued [1] that, in systems with an infinite number of the degrees of freedom, the Schrödinger picture of quantum mechanics may not be equivalent to the Heisenberg picture. The standard general proof of the equivalence of these two pictures may fail to be valid because, when an infinite number of the degrees of freedom is present, the formal unitary transformation between these two pictures may not exist in a rigorous sense. In [1], Dirac argued that it was the Heisenberg picture that was correct in the case of an infinite number of the degrees of freedom, while the Schrödinger picture was wrong. The two pictures are really equivalent only when the number of the degrees of freedom is finite.Recently, Faria et al [2] considered an example in which they explicitly obtained a discrepancy between the results obtained in the two pictures. Specifically, they considered a charged harmonic oscillator in 3 dimensions (having 3, i.e. a finite number of the degrees of freedom!) interacting with the electromagnetic field (having an infinite number of the degrees of freedom). For simplicity, they studied only the x-direction of the harmonic oscillator. In the Heisenberg picture, they quantized both the harmonic oscillator and the electromagnetic field and obtained that the average square of the position operator of the harmonic oscillator in the ground state is equal to x 2 =h/2mω 0 (where m is the mass of the harmonic oscillator and ω 0 is its frequency), the same result as if the interaction with the electromagnetic field was absent. In the Schrödinger picture, they used a semiclassical 1

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“…This result is in semiquantitative agreement with our classical stochastic calculation based on the Kramers theory with zero-point radiation. Finally, we would like to say that the direct inclusion of zero-point and thermal fluctuations into the Schrödinger equation [13] is a very delicate problem that is out of the scope of the present work.…”

Section: Comparison With Experimental Data and Conclusionmentioning

confidence: 99%

Tunneling and the Vacuum Zero-Point Radiation

França¹,

Gomes²,

Parra³

2007

Braz. J. Phys.

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We make a brief review of the Kramers escape rate theory for the probabilistic motion of a particle in a potential well U(x), and under the influence of classical fluctuation forces. The Kramers theory is extended in order to take into account the action of the thermal and zero-point random electromagnetic fields on a charged particle. The result is physically relevant because we get a non null escape rate over the potential barrier at low temperatures (T → 0). It is found that, even if the mean energy is much smaller than the barrier height, the classical particle can escape from the potential well due to the action of the zero-point fluctuating fields. These stochastic effects can be used to give a classical interpretation to some quantum tunneling phenomena. Relevant experimental data are used to illustrate the theoretical results.

show abstract

Critical assessment of the Schrödinger picture of quantum mechanics

Cited by 9 publications

References 19 publications

Tunneling as a Classical Escape Rate Induced by the Vacuum Zero-point Radiation

Tunneling as a Classical Escape Rate Induced by the Vacuum Zero-point Radiation

Comment on: “Critical assessment of the Schrödinger picture of quantum mechanics”

Tunneling and the Vacuum Zero-Point Radiation

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