Wave functions of a new functional kind has been proposed in this work for helium-like atoms. These functions depend explicitly on interelectronic and hyperspherical coordinates. The best ground state energy for the helium atom -2.903724376677a.u$-2.903724376677a.u$. has been calculated using the variational method with a basis including a single exponential parameter. To our knowledge, this is the best result so far using of hyperspherical coordinates. Comparable result has been obtained for the hydrogen anion. For helium atom, our best wave functions matched the Kato cusp conditions within an accuracy below 6.10^-4${6.10}^{-4}$. An important feature of proposed wave functions is the inclusion of negative powers of $R=\sqrt{(}{r}_1^2+r_2^2)$ in combination with positive powers of r₁₂$r_{12}$ into the wave function. We showed that this is necessary condition for proposed wave function to be a formal solution of Schrödinger equation.

在这项工作中，已经提出了一种新的功能类型的波函数，用于类氦原子。这些功能明确取决于电子间和超球面坐标。氦原子的最佳基态能量-2.903724376677au$--2.903724376677\mathrm{一个}。ü$。使用包含单个指数参数的基础的变分方法来计算“ A”。据我们所知，这是迄今为止使用超球面坐标的最佳结果。氢阴离子获得了可比的结果。对于氦原子，我们的最佳波动函数在6.10 ^-4以下的精度内与加藤尖峰条件相匹配${6.10}^{--4}$。所提出的波动函数的一个重要特征是包含了负功率。$\mathrm{[R}=\sqrt{（}{\mathrm{[R}}_{\mathrm{1个}}^{\mathrm{2个}}+{\mathrm{[R}}_{\mathrm{2个}}^{\mathrm{2个}}）$结合r _12的正幂${\mathrm{[R}}_{12}$进入波动功能。我们表明，这对于拟议的波动函数成为Schrödinger方程的形式化解是必要条件。