论文标题
在高斯扰动存在下，谐波振荡器的两个最低特征值
The two lowest eigenvalues of the harmonic oscillator in the presence of a Gaussian perturbation
论文作者
论文摘要
在本说明中，我们考虑了一个一维量子机械粒子，该粒子受到高斯电势扰动的抛物线的约束。由于相关的Birman-Schwinger操作员是痕量类别，因此可以利用Fredholm的决定因素，以计算由于高斯扰动的存在而与谐波振荡器不同的修饰的特征力。通过利用Wang的结果在谐波振荡器的四个特征函数的标量产品上，可以非常准确地评估两个最低的特征值作为耦合常数$λ$的函数。
In this note we consider a one-dimensional quantum mechanical particle constrained by a parabolic well perturbed by a Gaussian potential. As the related Birman-Schwinger operator is trace class, the Fredholm determinant can be exploited in order to compute the modified eigenenergies which differ from those of the harmonic oscillator due to the presence of the Gaussian perturbation. By taking advantage of Wang's results on scalar products of four eigenfunctions of the harmonic oscillator, it is possible to evaluate quite accurately the two lowest-lying eigenvalues as functions of the coupling constant $λ$.
