高斯势下Hill方程基态能量密度的形状
Shape of the ground state energy density of Hill's equation with nice Gaussian potential
摘要：
考虑希尔算子Q = -D^2 + q（x），其中势q（x）是周长为1的圆上的几乎必然连续且旋转不变的高斯过程。将经典Riccati映射看作测度变换，建立了基态能量密度函数的泛函积分公式，并确定了密度的形状.
英文摘要：
Consider Hill's operator Q = -D^2 + q(x) in which the potential q(x) is an almost surely continuous and rotation invariant Gaussian process on the circle of perimeter one. Viewing the classical Riccati map as a change of measure, we establish functional integral formulas for the probability density function of the ground state energy and also determine the density's shape.
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