A family of analytically solvable Schrödinger equations related by Levi-Civita transformation - Le , Dai Nam; Phan , Anh Luan; Luu , Phong Su; Phan , Ngoc Hung (Tạp chí Khoa học Trường Đại học Sư phạm Thành phố Hồ Chí Minh, 2019)
Some two-dimensional problems in non-relativistic quantum mechanics can connect to each other by certain spatial transformations such as Levi-Civita transformation. This property allows forming a series of two-dimensional problems into an interrelated family. Starting from two related problems namely Coulomb plus harmonic oscillator and sextic double-well anharmonic oscillator potentials, such family is constructed via repeatedly applying Levi-Civita transformations. Obviously, this family contains various of exactly analytically solvable problems. The quasi-exact solution for each unknown member of this family is also obtained and systematically investigated.