Schrödinger Equation for a Particle on a Curved Surface in an Electric and Magnetic Field

Ferrari, Giulio; Cuoghi, Giampaolo

doi:10.1103/physrevlett.100.230403

Cited by 183 publications

(228 citation statements)

References 20 publications

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“…Using the refined fundamental framework, we have reconsidered a spin-less charged particle bounded on the curved surface in an electromagnetic field [13]. The Coulomb gauge chosen for the electromagnetic field, the motion of the electromagnetic field and the Schrödinger equation are originally defined in the 3D subspace V N .…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Here the first term in the right hand side is the well-known geometric potential V g from the nonzero surface curvature, which is the same as in [13], the second term is the contribution of the first degree term of q 3 . In other words, the second term in Eq.…”

Section: Fig 2: (Color Online)mentioning

confidence: 99%

“…In a general form, the previously discussed system can be described by a canonical action integral [13,14,18] as…”

Section: A Spin-less Charged Particle Confined On 2d Curved Surfmentioning

confidence: 99%

“…Both the theoretical and experimental developments have attracted tremendous interest in the generalization of the JKC procedure to discuss a curved system with an electromagnetic field [12-14, 16, 17]. Under certain conditions, for the electromagnetic field a proper gauge should be chosen [13]. At the same time, the presence of the electromagnetic field determines that the motion equation of the vector potential for the electromagnetic field should be included [14].…”

Section: Introductionmentioning

confidence: 99%

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Quantum particle confined to a thin-layer volume: Non-uniform convergence toward the curved surface

Wang

Zong

2016

Annals of Physics

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We clearly refine the fundamental framework of the thin-layer quantization procedure, and further develop the procedure by taking the proper terms of degree one in q3 (q3 denotes the curvilinear coordinate variable perpendicular to curved surface) back into the surface quantum equation. The well-known geometric potential and kinetic term are modified by the surface thickness. Applying the developed formalism to a toroidal system obtains the modification for the kinetic term and the modified geometric potential including the influence of the surface thickness.

show abstract

Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Fig 2: (Color Online)mentioning

confidence: 99%

“…In a general form, the previously discussed system can be described by a canonical action integral [13,14,18] as…”

Section: A Spin-less Charged Particle Confined On 2d Curved Surfmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum particle confined to a thin-layer volume: Non-uniform convergence toward the curved surface

Wang

Zong

2016

Annals of Physics

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“…In fact, the situation is far more complicated than what is anticipated. This is because in quantum mechanics for motion on the hypersurface, there is a curvature induced potential [2][3][4][5] that has no classical correspondence, and we can by no mean assume that same form of the Ehrenfest theorem for the time derivative of mean value of the momentum applies.…”

confidence: 99%

Heisenberg equation for a nonrelativistic particle on a hypersurface: From the centripetal force to a curvature induced force

Lian

Liu

2017

AIP Advances

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In classical mechanics, a nonrelativistic particle constrained on an N − 1 curved hypersurface embedded in N flat space experiences the centripetal force only. In quantum mechanics, the situation is totally different for the presence of the geometric potential. We demonstrate that the motion of the quantum particle is "driven" by not only the the centripetal force, but also a curvature induced force proportional to the Laplacian of the mean curvature, which is fundamental in the interface physics, causing curvature driven interface evolution.

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Electron on a cylinder with topological defects in a homogeneous magnetic field

Filgueiras

Oliveira

2011

Annalen der Physik

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In this work we study the effects of the geometry and topology of a cylinder on the energy levels of an electron moving in a homogeneous magnetic field. We consider the existence of topological defects as a screw dislocation and a disclination. When we take the region of movement as the full cylindrical surface, we find that, by increasing the strength of the screw dislocation, the dispersion on the electronic energy levels is affected and monotonically increasing. For an electron moving in an almost flat region we show that the dispersion on the Landau levels decrease monotonically as we increase the strength of the screw dislocation. The lowest Landau level can reach a zero value, leaving the energy of the system solely given by the geometry of the cylinder, which does not depend on the magnetic field. In both situations, as we change the deficit angle of the disclination, we observe that the energy levels are shifted and the magnitude of such shift depends on the magnetic field. The Landau levels for a flat sample are recovered in the limit of an infinite cylinder radius.

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Schrödinger Equation for a Particle on a Curved Surface in an Electric and Magnetic Field

Cited by 183 publications

References 20 publications

Quantum particle confined to a thin-layer volume: Non-uniform convergence toward the curved surface

Quantum particle confined to a thin-layer volume: Non-uniform convergence toward the curved surface

Heisenberg equation for a nonrelativistic particle on a hypersurface: From the centripetal force to a curvature induced force

Electron on a cylinder with topological defects in a homogeneous magnetic field

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