Geodesic
Electric dipole in a~magnetic field: Bound states without classical turning points
Teoretičeskaâ i matematičeskaâ fizika, Tome 117 (1998) no. 2, pp. 189-205

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We show that both rigid and nonrigid dipoles can be trapped by an uniform external magnetic field in classical mechanics. The trapped states of the dipole present a nontrivial example of classical bound states embedded in a continuum (BSEC) that can be treated as analogues of quantum BSECs. For example, the classical motion of the dipole is confined to a finite region in space although there are no classical turning points. We also examine the quantum motion of the dipole in a magnetic field and show that for the most natural choices of the parameters, no quantum BSEC solutions exist. The possibilities of experimental investigations of BSECs are discussed. 
@article{TMF_1998_117_2_a2,
     author = {D. L. Pursey and N. A. Sveshnikov and A. M. Shirokov},
     title = {Electric dipole in a~magnetic field: {Bound} states without classical turning points},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {189--205},
     publisher = {mathdoc},
     volume = {117},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1998_117_2_a2/}
}
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D. L. Pursey; N. A. Sveshnikov; A. M. Shirokov. Electric dipole in a~magnetic field: Bound states without classical turning points. Teoretičeskaâ i matematičeskaâ fizika, Tome 117 (1998) no. 2, pp. 189-205. http://geodesic.mathdoc.fr/item/TMF_1998_117_2_a2/