Reply to “Comments on Bouda and Djama's ‘Quantum Newton's Law’”

Bouda, A.; Djama, T.

doi:10.1016/s0375-9601(02)00277-3

Cited by 12 publications

(33 citation statements)

References 7 publications

(28 reference statements)

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“…It can also be obtained by applying (8) or (11). As expected, it is a fourth order differential equation.…”

Section: The Quantum Law Of Motionmentioning

confidence: 80%

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From a Mechanical Lagrangian to the Schrödinger Equation: A Modified Version of the Quantum Newton Law

Bouda

2003

Int. J. Mod. Phys. A

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In the one-dimensional stationary case, we construct a mechanical Lagrangian describing the quantum motion of a non-relativistic spinless system. This Lagrangian is written as a difference between a function T , which represents the quantum generalization of the kinetic energy and which depends on the coordinate x and the temporal derivatives of x up the third order, and the classical potential V (x). The Hamiltonian is then constructed and the corresponding canonical equations are deduced. The function T is first assumed arbitrary. The development of T in a power series together with the dimensional analysis allow us to fix univocally the series coefficients by requiring that the well-known quantum stationary Hamilton-Jacobi equation be reproduced. As a consequence of this approach, we formulate the law of the quantum motion representing a new version of the quantum Newton's law. We also analytically establish the famous Bohm's relation µẋ = ∂S0/∂x outside of the framework of the hydrodynamical approach and show that the well-known quantum potential, although it is a part of the kinetic term, it plays really a role of an additional potential as assumed by Bohm.

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“…It can also be obtained by applying (8) or (11). As expected, it is a fourth order differential equation.…”

Section: The Quantum Law Of Motionmentioning

confidence: 80%

“…In Ref. [11], it is shown that the resulting trajectories depend on the choice of the couple of solutions of the SE used in the expression of S 0 . This represents an unsatisfactory feature since the mathematical choices affect the physical results.…”

Section: Introductionmentioning

confidence: 99%

From a Mechanical Lagrangian to the Schrödinger Equation: A Modified Version of the Quantum Newton Law

Bouda

2003

Int. J. Mod. Phys. A

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“…Molecular hydrogen and carbon dioxide have been chosen as benchmarking systems for fundamental studies as well as for medical applications. Particular attention is given to the emission characteristics of the low-energy electrons, which are very reactive in biological tissue [1].…”

Section: Introductionmentioning

confidence: 99%

Fragmentation of molecules by fast ion impact

Dimopoulou¹,

Haag²,

Moshammer³

et al. 2007

J. Phys.: Conf. Ser.

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Abstract. Single ionization of simple molecules, e.g. H 2 , CO 2 , by fast charged particle impact has been studied using a reaction microscope. By measuring the momenta of the emitted electron and the recoil ionic fragment in coincidence, channel-selective low-energy electron spectra have been recorded. The experimental cross sections will be presented, compared with the predictions of state-of-the-art CDW-EIS calculations and discussed in terms of molecular effects such as (i) autoionization and predissociation channels, (ii) interference patterns resulting from the two-center geometry of the diatomic molecule, in analogy to Young's double-slit experiment and (iii) dependence of the electron emission on the orientation of the molecular axis.

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“…On the other hand, many suggestions to formulate the quantum trajectory equations were proposed [3,4,15,17,18,19,20]. In a recent paper [21], the QSHJE in one dimension, 1 2m…”

Section: Introductionmentioning

confidence: 99%

The Three-Dimensional Quantum Hamilton-Jacobi Equation and Microstates

Bouda

Meziane

2006

Int J Theor Phys

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In a stationary case and for any potential, we solve the three-dimensional quantum Hamilton-Jacobi equation in terms of the solutions of the corresponding Schrödinger equation. Then, in the case of separated variables, by requiring that the conjugate momentum be invariant under any linear transformation of the solutions of the Schrödinger equation used in the reduced action, we clearly identify the integration constants successively in one, two and three dimensions. In each of these cases, we analytically establish that the quantum Hamilton-Jacobi equation describes microstates not detected by the Schrödinger equation in the real wave function case.

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Reply to “Comments on Bouda and Djama's ‘Quantum Newton's Law’”

Cited by 12 publications

References 7 publications

From a Mechanical Lagrangian to the Schrödinger Equation: A Modified Version of the Quantum Newton Law

From a Mechanical Lagrangian to the Schrödinger Equation: A Modified Version of the Quantum Newton Law

Fragmentation of molecules by fast ion impact

The Three-Dimensional Quantum Hamilton-Jacobi Equation and Microstates

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