We present and discuss numerical solutions to a two-body quantum bound state problem closely related to that of the hydrogen atom and the deuterium nucleus. The forces binding the particles of our system are Yukawa forces, which fall off with distance faster than the Coulomb force and arise for non-relativistic particles whose interactions are mediated by massive scalar or vector particles; the Coulomb force arises in the limit of massless mediators such as photons. We use the solutions to explain several features of deuterium. We also present heuristic estimates of ground state energies and energy level degeneracy breaking. Studying this Yukawa two-body system provides insights into hydrogen, deuterium, and two-body bound states, generally. We describe our undergraduate-accessible procedure for numerically solving non-relativistic two-body bound state problems with mathematica in the appendix.

中文翻译：

---

通过汤川力的两体结合态以及氢和氘的观点

我们提出并讨论了与氢原子和氘原子核紧密相关的两体量子束缚态问题的数值解。束缚我们系统粒子的力是汤川力，它以比库仑力更快的距离下降，并且是由相对论性粒子产生的，其相互作用是由大标量或矢量粒子介导的。库仑力是在无质量的介质（例如光子）的极限范围内产生的。我们使用解决方案来解释氘的几个特征。我们还提出了基态能量和能级简并性破坏的启发式估计。通常，对这种Yukawa两体系统的研究可以提供有关氢，氘和两体结合态的见解。附录中的mathematica。