### A family of analytically solvable Schrödinger equations related by Levi-Civita transformation

*Le Dai Nam, Phan Anh Luan, Luu Phong Su, Phan Ngoc Hung*

#### Tóm tắt

*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.*

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Tạp chí của Trường Đại học Sư phạm Thành phố Hồ Chí Minh ; ISSN: 1859 -3100