By use of the well-known truncating series method,A program for calculating the Schr?dinger exact solutions of quantum gate by two ions confined in a linear Paul trap is presented. The lower energy's state function for center of mass is analyzed. Probability distributing grawing is given. We calculate quantum state of variance in relatively position △r²＞ h/2 and quantum state of variance in relatively momentum △p²＜ h/2,the variance in position and momentum given by the Heisenberg uncertainty principle △r·△p＞h/2.It is a condition for squeezed states. We conclude that with center of mass in ground state,the quantum states of two ions in relatively position are squeezed states,and the quantum state of two ions is an entanglement state. Uncertainty of quantum measurement and entanglement must be consider in experiment.