The 3D quantum stationary Hamilton–Jacobi equation for symmetrical potentials

Djama, T.

doi:10.1088/0031-8949/75/1/012

Cited by 4 publications

(22 citation statements)

References 12 publications

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“…Whatever the expression of the reduced action S 0 in terms of S 0x , S 0y and S 0z , we see that the form (22) cannot reproduce (7). In addition, it is stated in [14] that the above form (21) is justified in [4,5]. We emphasize that this is wrong.…”

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confidence: 76%

“…Admittedly the separated variable case is particular but relation (7) continues to work and never reduces to (22) which follows straightforwardly from (21). Thus, contrary to the statement made in [14], relations (21) and (22) are not in agreement with the equivalence postulate of quantum mechanics [4,5,6,7] as they are not with Bohmian mechanics.…”

mentioning

confidence: 81%

“…In [13] and [14], the extension of this solution to higher dimensions in the separated variable case is investigated and the results are contradictory. The aim of this paper is to provide new insights into the construction of the reduced action in higher dimensions.…”

Section: Introductionmentioning

confidence: 99%

“…The last comment is to say that the procedure used in the construction of the reduced action in [14] leads to a result which does not contain a complete information about the quantum motion. To justify this, some mathematical details are necessary.…”

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confidence: 99%

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The Quantum Reduced Action in Higher Dimensions

Bouda

2008

Int J Theor Phys

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The solution with respect to the reduced action of the one-dimensional stationary quantum Hamilton-Jacobi equation is well known in the literature. The extension to higher dimensions in the separated variable case was proposed in contradictory formulations. In this paper we provide new insights into the construction of the reduced action. In particular, contrary to the classical mechanics case, we analytically show that the reduced action constructed as a sum of one variable functions does not contain a complete information about the quantum motion. In the same context, we also make some observations about recent results concerning quantum trajectories. Finally, we will examine the conditions in which microstates appear even in the case where the wave function is complex.

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confidence: 76%

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confidence: 81%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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The Quantum Reduced Action in Higher Dimensions

Bouda

2008

Int J Theor Phys

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“…The quantum Hamilton-Jacobi theory and antisymmetric mechanics were connected in [25]. Numerical schemes for conservation laws via Hamilton-Jacobi equations were investigated in [26] and an accurate computational method for the one-dimensional quantum Hamilton-Jacobi equation was obtained in [27]. The 3D quantum stationary Hamilton-Jacobi equation for symmetric potentials was investigated in [28].…”

Section: Introductionmentioning

confidence: 99%

Hamilton–Jacobi and fractional like action with time scaling

et al. 2011

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This paper represents the Hamilton-Jacobi formulation for fractional variational problem with fractional like action written as an integration over a time scaling parameter. Also we developed the fractional Hamiltonian formulation for the fractional like action. In all the given calculations, the most popular Riemann-Liouville (RL) and Caputo fractional derivatives are employed. An example illustrates our approach.

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The 3D quantum law of motion and the 3D quantum trajectories

Djama¹

2007

Phys. Scr.

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In this paper, we introduced the 3D-Quantum Stationary Hamilton Jacobi Equation for a central potential, and established the 3D quantum law of motion of an electron in the presence of such a potential. We established a system of three differential equations from which, and as a numerical application, we plotted the 3D quantum trajectories of the Hydrogen's electron for the ground state and two excited states. we did a comparison between a supposed classical trajectory of the hydrogen electron and the corresponding QTs. We found out that for a particular set of the hidden variables, the QT is close in its shape to the classical one.

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The 3D quantum stationary Hamilton–Jacobi equation for symmetrical potentials

Cited by 4 publications

References 12 publications

The Quantum Reduced Action in Higher Dimensions

The Quantum Reduced Action in Higher Dimensions

Hamilton–Jacobi and fractional like action with time scaling

The 3D quantum law of motion and the 3D quantum trajectories

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