Abstract
Measuring energies in units of the Rydberg energy E ∞, lengths in units of the Bohr radius a 0, and the magnetic field strength in units of B 0, the Hamiltonian of an electron in a static Coulomb potential and in a uniform magnetic field then reads for spin-down states
where the magnetic field is assumed to point in the z-direction and ϱ 2 = x 2+y 2. The energies of the corresponding spin-up states are obtained by simply adding 4β. The eigenstates of (3.1) can be classified according to z-parity π and the z-component l z of orbital angular momentum, which are exact symmetries of H, but in general no further separation of the two-dimensional problem is possible.
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© 1994 Springer-Verlag Berlin Heidelberg
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Ruder, H., Wunner, G., Herold, H., Geyer, F. (1994). Methods of Solution for the Magnetized Coulomb Problem. In: Atoms in Strong Magnetic Fields. Astronomy and Astrophysics Library. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78820-8_3
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DOI: https://doi.org/10.1007/978-3-642-78820-8_3
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