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arXiv 1402.2163quant-ph
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表面附近电子的塞曼位移

Zeeman shift of an electron trapped near a surface

Robert Bennett, Claudia Eberlein

摘要:

研究了弱磁场中简谐囚禁势对电子自旋能本征值的边界相关修正。电磁场通过在材料表面服从麦克斯韦边界条件的简正模展开进行量子化。我们将电子耦合到这个光子场和狄拉克方程中的经典磁场,我们对其应用么正的Foldy-Wouthuysen变换,以生成所需阶的哈密顿量的非相对论近似。我们得到了一个电子在简谐势和经典磁场双重约束下的薛定谔本征态,然后用二阶微扰理论计算了表面改性量子化场引起的自旋能移。我们发现,在一组广义朗道跃迁的本征频率的极点在弱磁场中的紧谐波约束的极限中对能量移动给出了占主导地位的振荡贡献,这也使得能量移动比磁矩更适合于物理上有意义的解释。

英文摘要:

Boundary dependent corrections to the spin energy eigenvalues of an electron in a weak magnetic field and confined by a harmonic trapping potential are investigated. The electromagnetic field is quantized through a normal mode expansion obeying the Maxwell boundary conditions at the material surface. We couple the electron to this photon field and a classical magnetic field in the Dirac equation, to which we apply the unitary Foldy-Wouthuysen transformation in order to generate a non-relativistic approximation of the Hamiltonian to the desired order. We obtain the Schrödinger eigenstates of an electron subject to double confinement by a harmonic potential and a classical magnetic field, and then use these within second-order perturbation theory to calculate the spin energy shift that is attributable to the surface-modified quantized field. We find that a pole at the eigenfrequency of a set of generalized Landau transitions gives dominant oscillatory contributions to the energy shift in the limit of tight harmonic confinement in a weak magnetic field, which also make the energy shift preferable to the magnetic moment for a physically meaningful interpretation.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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