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

Lian, D. K.; Hu, Liangdong; Liu, Q. H.

doi:10.48550/arxiv.1707.08165

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“…The details will be published elsewhere. We mention here that a similar conclusion was obtained in the work [29,30] by a completely different approach. The explicit form for the Hermitian velocity operator reads:…”

Section: Spin Force On the Oscillator On A Spheresupporting

confidence: 90%

Spin force and torque in non-relativistic Dirac oscillator on a sphere

Shikakhwa

2018

Physics Letters A

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The spin force operator on a non-relativistic Dirac oscillator ( in the non-relativistic limit the Dirac oscillator is a spin one-half 3D harmonic oscillator with strong spin-orbit interaction) is derived using the Heisenberg equations of motion and is seen to be formally similar to the force by the electromagnetic field on a moving charged particle . When confined to a sphere of radius R, it is shown that the Hamiltonian of this non-relativistic oscillator can be expressed as a mere kinetic energy operator with an anomalous part. As a result, the power by the spin force and torque operators in this case are seen to vanish. The spin force operator on the sphere is calculated explicitly and its torque is shown to be equal to the rate of change of the kinetic orbital angular momentum operator, again with an anomalous part. This, along with the conservation of the total angular momentum, suggest that the spin force exerts a spin-dependent torque on the kinetic orbital angular momentum operator in order to conserve total angular momentum. The presence of an anomalous spin part in the kinetic orbital angular momentum operator gives rise to an oscillatory behavior similar to the Zitterbewegung. It is suggested that the underlying physics that gives rise to the spin force and the Zitterbewegung is one and the same in NRDO and in systems that manifest spin Hall effect.

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Section: Spin Force On the Oscillator On A Spheresupporting

confidence: 90%

Spin force and torque in non-relativistic Dirac oscillator on a sphere

Shikakhwa

2018

Physics Letters A

View full text Add to dashboard Cite

show abstract

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

Cited by 1 publication

References 1 publication

Spin force and torque in non-relativistic Dirac oscillator on a sphere

Spin force and torque in non-relativistic Dirac oscillator on a sphere

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