“…Particularly, Levi-Civita transformation (Levi-Civita, 1906) has been widely used as an efficient tool to connect the Schrödinger equations which describe two-dimensional motions under the influence of some central potentials, e.g Coulomb and harmonic oscillator potentials (Le & Nguyen, 1993) or Coulomb potential plus harmonic oscillator term (C+HO) and sextic double-well anharmonic oscillator (sextic DWAO) (Hoang-Do, Pham & Le, 2013). The former problem, which arises from two-dimensional hydrogen atom model under presence of a homogeneous magnetic field, has been analytically solved both in recurrence form (Taut, 1995) and in compact form (Le, Hoang & Le, 2017) while the exact analytical solution for later one is also obtained in compact form via the inspiration of one-dimension case (Le, Hoang & Le, 2018). Hence, repeatedly applying Levi-Civita transformation into C+HO and sextic DWAO problems can leads us to other problems whose analytical solution can be exactly obtained in compact form as the same as known ones shown by Le, Hoang & Le (2017, 2018.…”