In this paper, we solve the massive scalar field in the Reissner–Nordström spacetime. The scalar field in the Reissner–Nordström spacetime has both bound states and scattering states. For bound states, we solve the bound-state wave function and the eigenvalue spectrum. For scattering states, we solve the scattering wave function and give an explicit expression for scattering phase shift by the integral equation method. Especially, we introduce the tortoise coordinate for the Reissner–Nordström spacetime. Moreover, in the calculation of scattering cross sections, we encounter a difficulty in partial sum approximation. If the sum of partial waves cannot be performed exactly, one has to turn to the partial sum approximation which approximates a function by the first several terms of the series. However, in the partial sum approximation there exists an incorrect oscillation which cannot be eliminated by keeping more terms. In the appendix we suggest an approach for eliminating such oscillations in the partial sum.

在本文中，我们解决了 Reissner-Nordström 时空中的大量标量场。Reissner-Nordström 时空中的标量场具有束缚态和散射态。对于束缚态，我们求解束缚态波函数和特征值谱。对于散射态，我们求解散射波函数，并通过积分方程法给出散射相移的显式表达式。特别是，我们引入了 Reissner-Nordström 时空的乌龟坐标。此外，在散射截面的计算中，我们遇到了部分求和近似的困难。如果部分波的求和不能精确执行，则必须转向部分求和近似，它通过级数的前几项来近似函数。然而，在部分和近似中存在不正确的振荡，不能通过保留更多项来消除。在附录中，我们提出了一种消除部分和中此类振荡的方法。