磁场中的相互作用电子：跟踪势和Jastrow乘积波函数
Interacting electrons in magnetic fields: Tracking potentials and Jastrow-product wavefunctions
摘要：
非均匀磁场中相互作用的无自旋电子气的薛定谔方程，当磁场中的涨落跟踪标势中的涨落时，存在一个Jastrow乘积形式的精确解。对于二维电子气中的跟踪实现，最低朗道能级的简并持续存在，并且"跟踪“解跨越基态子空间。在分数量子霍尔问题的背景下，Laughlin波函数被证明是一个跟踪解决方案。还构造了屏蔽库仑相互作用的跟踪解。由此产生的波函数提出的变分波函数具有潜在的更低的能量的情况下，不可忽略的朗道能级混合比Laughlin函数。
英文摘要：
The Schrodinger equation for an interacting spinless electron gas in a nonuniform magnetic field admits an exact solution in Jastrow product form when the fluctuations in the magnetic field track the fluctuations in the scalar potential. For tracking realizations in a two-dimensional electron gas, the degeneracy of the lowest Landau level persists, and the ``tracking'' solutions span the ground state subspace. In the context of the fractional quantum Hall problem, the Laughlin wave function is shown to be a tracking solution. Tracking solutions for screened Coulomb interactions are also constructed. The resulting wavefunctions are proposed as variational wave functions with potentially lower energy in the case of non-negligible Landau level mixing than the Laughlin function.
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