Eigen Wavefunctions of a Charged Particle Moving in a Self-Linking Magnetic Field

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dc.creatorChiou, Dah-Wei
dc.creatorLee, Dung-Hai
dc.creatorHsiang, Wu-Yi
dc.date2004-11-11
dc.date.accessioned2026-07-07T04:31:37Z
dc.date.available2026-07-07T04:31:37Z
dc.descriptionIn this paper we solve the one-particle Schrödinger equation in a magnetic field whose flux lines exhibit mutual linking. To make this problem analytically tractable, we consider a high-symmetry situation where the particle moves in a three-sphere $(S^3)$. The vector potential is obtained from the Berry connection of the two by two Hamiltonian $H(ř)=\hat{h}(ř) \cdot\vecσ$, where $ř\in S^3$, $\hat{h}\in S^2$ and $\vecσ$ are the Pauli matrices. In order to produce linking flux lines, the map $\hat{h}:S^3\to S^2$ is made to possess nontrivial homotopy. The problem is exactly solvable for a particular mapping ($\hat{h}$) . The resulting eigenfunctions are SO(4) spherical harmonics, the same as those when the magnetic field is absent. The highly nontrivial magnetic field lifts the degeneracy in the energy spectrum in a way reminiscent of the Zeeman effect.
dc.description24 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math-ph/0411044
dc.identifierhttp://arxiv.org/abs/math-ph/0411044
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57884
dc.subjectMathematical Physics
dc.subject58J28; 70S15
dc.titleEigen Wavefunctions of a Charged Particle Moving in a Self-Linking Magnetic Field
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