A quantum stationary wave has been examined in an exchange field, which induces the force of the form $F(r)=f_{2}(1/r^{2}-f_{1}/r)$. For the Coulomb attraction in hydrogen atom, the inexplicable discrepancy (0.0023 MHz) between the theoretical and experimental frequencies for its $^{1}S_{1/2}$ has been verified. It is found that the tiny $f_{1}$ is $7.45\times10^{-12}a_{1}$$^{-1}$($a_{1}$ is the 1st Bohr radius). Meanwhile, when such an $f_{1}$ is considered in the $n=2$ Lamb shift, it causes -0.034 MHz difference, which is in good agreement with the deviation of -0.039 MHz between the experimental and one of the theoretical predictions. Similar of searchings are made for the Lande $g$ factor for the $H_{\beta}$ spectrum. This $f_{1}$ contributes a ratio $\Delta g/g=5.58\times10^{-11}$ and makes both the experiment and theory well agreed within the experimental relative uncertainty $\pm4\times10^{-12}$. In other words, these phenomena can be treated as the reliable physical evidences for the existence of the same repulsion. More importantly, they consistently and strongly imply that the maximum radius for the Coulomb attraction in hydrogen atom can not exceed 7.11$m$ (if extrapolated). In addition, this analysis prompts us similar cases probably occur in the gravitation because it is also an exchange field, and the repulsion at remote distance may be one kind of dark energy that may have been ignored.