From Micro to Macro Quantum Systems

Wan, K. Kong

doi:10.1142/p427

Cited by 10 publications

(8 citation statements)

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“…For a good introduction on the importance of Sobolev spaces in quantum physics we refer the reader to [48], where the conection between Sobolev spaces and absolute continuity is considered too.…”

Section: Regarding H *mentioning

confidence: 99%

Free-fall in a uniform gravitational field in noncommutative quantum mechanics

Castello-Branco

Martins

2010

Journal of Mathematical Physics

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4-dimensional spin-foam model with quantum Lorentz group J. Math. Phys. 52, 072501 (2011) Attributing sense to some integrals in Regge calculus J. Math. Phys. 52, 022502 (2011) When do measures on the space of connections support the triad operators of loop quantum gravity? J. Math. Phys. 52, 012503 (2011) Some results concerning the representation theory of the algebra underlying loop quantum gravity J. Math. Phys. 52, 012502 (2011) Additional information on J. Math. Phys. We study the free-fall of a quantum particle in the context of noncommutative quantum mechanics ͑NCQM͒. Assuming noncommutativity of the canonical type between the coordinates of a two-dimensional configuration space, we consider a neutral particle trapped in a gravitational well and exactly solve the energy eigenvalue problem. By resorting to experimental data from the GRANIT experiment, in which the first energy levels of freely falling quantum ultracold neutrons were determined, we impose an upper-bound on the noncommutativity parameter. We also investigate the time of flight of a quantum particle moving in a uniform gravitational field in NCQM. This is related to the weak equivalence principle. As we consider stationary, energy eigenstates, i.e., delocalized states, the time of flight must be measured by a quantum clock, suitably coupled to the particle. By considering the clock as a small perturbation, we solve the ͑stationary͒ scattering problem associated and show that the time of flight is equal to the classical result, when the measurement is made far from the turning point. This result is interpreted as an extension of the equivalence principle to the realm of NCQM.

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Section: Regarding H *mentioning

confidence: 99%

Free-fall in a uniform gravitational field in noncommutative quantum mechanics

Castello-Branco

Martins

2010

Journal of Mathematical Physics

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“…(Of course if one considers compact spaces, for example physics on a circle with periodic boundary conditions, then all states are localised and can be degenerate, see for example [5]). …”

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“…These have been studied by a number of authors, and it has also been suggested that some of the singular potentials approximate certain physical situations in molecular chemistry [4] and elsewhere [5]. However, it should be noted that singular potentials by themselves do not guarantee degeneracy [4,5].…”

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confidence: 99%

“…The expression (3) is ill-defined at places where the wave function vanishes, and it was argued that if the potential was singular at a node of the wave functions then one could produce degenerate bound states [3]. These have been studied by a number of authors, and it has also been suggested that some of the singular potentials approximate certain physical situations in molecular chemistry [4] and elsewhere [5]. However it should be noted that singular potentials by themselves do not guarantee degeneracy [4,5].…”

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Can degenerate bound states occur in one-dimensional quantum mechanics?

Kar

Parwani

2007

Europhys. Lett.

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We point out that bound states, degenerate in energy but differing in parity, may form in one dimensional quantum systems even if the potential is non-singular in any finite domain. Such potentials are necessarily unbounded from below at infinity and occur in several different contexts, such as in the study of localised states in brane-world scenarios. We describe how to construct large classes of such potentials and give explicit analytic expressions for the degenerate bound states.Some of these bound states occur above the potential maximum while some are below. Various unusual features of the bound states are described and after highlighting those that are ansatz independent, we suggest that it might be possible to observe such parity-paired degenerate bound states in specific mesoscopic systems.

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“…Recently Saglam and Boyacioglu [3] calculated semiclassically, the quantized magnetic flux through the Landau orbits of an electron including the effect of the spinning motion. They showed that the spin contribution to the quantized flux is equal to ( time pointed out by Wan [5] that the intrinsic quantum flux of electron must be related to the hidden variables in quantum mechanics. In Appendix I we show that the conservation of the angular momentum has two elements, namely, the conservation of the spin angular momentum and the conservation of the quantum flux.…”

Section: Introductionmentioning

confidence: 94%

Explanation of the Hidden Variables in the Electron-Positron Annihilation Process in Terms of the Quantum Entanglement and the Conservation of Flux Quantum

Sağlam¹,

Gür²,

Yilmaz³

2018

JMP

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We show that the electron-positron annihilation process resulting with the creation of two gamma photons cannot be fully determined without the conservation of the angular momentum which has two elements, namely, the conservation of the spin angular momentum and the conservation of the quantum flux which work as the conservation of the magnetic moments as well. The conservation of the quantum flux has never been considered so far for any collision process. We show that the missing conservation rule in the above process is the conservation of the total quantum flux which is the hidden variable of that process. By using the quantum entanglement together with the conservation of the quantum flux we show that the initial and the final states of this collision are fully determined. We also show that each of the gamma photons created in the end carries a quantum flux of 0 hc e ±Φ = ± with itself along the propagation direction. Here the (+) and (−) signs correspond to the right hand and left circular helicity, respectively.

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From Micro to Macro Quantum Systems

Cited by 10 publications

References 0 publications

Free-fall in a uniform gravitational field in noncommutative quantum mechanics

Free-fall in a uniform gravitational field in noncommutative quantum mechanics

Can degenerate bound states occur in one-dimensional quantum mechanics?

Explanation of the Hidden Variables in the Electron-Positron Annihilation Process in Terms of the Quantum Entanglement and the Conservation of Flux Quantum

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