磁单极存在时Pauli方程的自伴延拓
Self-Adjoint Extensions of the Pauli Equation in the Presence of a Magnetic Monopole
摘要：
本文讨论了具有自旋的非相对论电子在阿贝尔磁链存在下的哈密顿量，并指出在最低两个角动量模中它不是自伴的。然后，我们使用冯诺依曼的自伴扩张理论，构造一个自伴算子具有相同的功能形式。一般来说，这个算符会有最低两个角动量模混合的本征态，从而消除了角动量守恒。然而，与狄拉克方程的解的一致性限制了恢复角动量守恒的可能性。由于同样的效果发生在一个无自旋粒子具有足够的吸引力平方反比的潜力，我们也研究这个系统。我们使用这个简单的哈密顿比较对应于一个特定的自伴扩展的本征函数满足边界条件与概率守恒。
英文摘要：
We discuss the Hamiltonian for a nonrelativistic electron with spin in the presence of an abelian magnetic monopole and note that it is not self-adjoint in the lowest two angular momentum modes. We then use von Neumann's theory of self-adjoint extensions to construct a self-adjoint operator with the same functional form. In general, this operator will have eigenstates in which the lowest two angular momentum modes mix, thereby removing conservation of angular momentum. However, consistency with the solutions of the Dirac equation limits the possibilities such that conservation of angular momentum is restored. Because the same effect occurs for a spinless particle with a sufficiently attractive inverse square potential, we also study this system. We use this simpler Hamiltonian to compare the eigenfunctions corresponding to a particular self-adjoint extension with the eigenfunctions satisfying a boundary condition consistent with probability conservation.
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