minimum value of $V_\ell$ increases linearly with $\ell$.[]{data-label="eff_pot"}](Kin-cent-potential.pdf)

Physically, electrons circulating with positive angular momentum in the presence of a magnetic field directed in the positive $z$ direction cost energy, whereas those with negative angular momentum do not. This is consistent with the classical idea that electrons speed up or slow down depending on whether they are circulating with positive or negative angular momentum, respectively.[@griffiths99] This effective potential is illustrated in Fig. (\[eff\_pot\]).

[Fock-Darwin States]{}
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Fock first addressed the problem of the eigenstates of a charged particle in a uniform magnetic field in 1928.[@fock28] He discovered a generally non-degenerate spectrum, particularly because the charged particle was confined to a parabolic potential. Somewhat later Landau[@landau30] examined a similar (simpler) problem in free space, and found a degenerate spectrum given in Eq. (\[energy\_landau\_level\]), which now bears his name. A year later, Darwin[@darwin31] independently obtained results similar to those of Fock, and figures displaying energy levels as a function of applied field are now called Fock-Darwin Spectra. The presence of a confining potential in the form of a parabolic trap requires very little additional work, so we now describe this work, also featured, for example, in Ref. \[\].

In the Symmetric gauge, 