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Rewriting the equation by using B = ∇ × A and e = −|e| (electron charge) leads to a Schr¨odinger like equation:

$$i\frac{\partial \phi}{\partial t} =[ \frac{1}{2m} (-i∇ + |e|A)^2 + \frac{|e|}{2m} σ.B - |e|φ ]\phi$$

How did the B suddenly appear in the second equation? Alll help will be greatly appreciated.

Source: http://physics.sharif.edu/~qmech/puppel.pdf ,Page 21.