An anharmonic oscillator $T\left(q\right)=-\frac{d^2}{d{x}^2}+x^2+q\left(x\right)$ on the half-axis $0\le x<\infty$ with the Neumann boundary condition is considered. By means of transformation operators, the direct and inverse spectral problems are studied. We obtain the main integral equations of the inverse problem and prove that the main equation is uniquely solvable. An effective algorithm for reconstruction of perturbed potential is indicated.

中文翻译：

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具有Neumann边界条件的半轴上非谐振子的反谱问题

非谐振荡器 $Ť（q）=--\frac{d^2}{d{X}^2}+X^2+q（X）$ 在半轴上 $0\le X<\infty$考虑诺伊曼边界条件。借助变换算子，研究了正谱和反谱问题。我们获得了反问题的主要积分方程，并证明了该主要方程是唯一可解的。指出了一种重构扰动电位的有效算法。