The analytical transfer matrix method (ATMM) is applied to calculating the critical radius rc and the dipole linear relation between rc1/2 and the quantum number n(r) for a fixed angular quantum number l, moreover, the three bounds of αd (αKd, αBd, αUd) satisfy an inequality: αdK ≤αBd ≤αdU. A comparison between the ATMM, the exact numerical analysis, and the variational wavefunctions shows that our method works very well in the systems.