# The quantum-mechanical description of an electron motion in a magnetic monopole field

The quantum-mechanical motion problem of an electron in electric field of the nucleus is well known. The quantum-mechanical description of electron motion in a magnetic field is also not difficult, since it needs to solve the Schrödinger equation of the form: $$\frac{(\hat p + eA)^2} {2m} \psi = E \psi$$ But if we want to consider the motion of an electron in a magnetic monopole field, the difficulty arises because the definition of the vector potential in the whole space. See, for example. Was this problem solved? What interesting consequences derived from this task? (for energy levels, angular momentum etc.)

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This gives you coherent state representation for angular momentum. – Slaviks Mar 16 '12 at 21:54
The difficulty is not in the vector potential--- you can just use a Dirac string. The difficulty is getting the actual solution. – Ron Maimon Apr 15 '12 at 7:42