Harko, TiberiuTiberiuHarkoMak, Man KwongMan KwongMak2026-10-092026-10-092021Harko, Tiberiu; Mak, Man Kwong (2021). ANALYTICAL SOLUTIONS OF THE ONE-DIMENSIONAL SCHR ODINGER EQUATION WITH POSITION-DEPENDENT MASS. ROMANIAN JOURNAL OF PHYSICS, 66(7-8), 116.1221-146Xhttps://hdl.handle.net/20.500.12740/25130The study of the Schr\"{o}dinger equation with the position-dependent effective mass has attracted a lot of attention, due to its applications in many fields of physics, including the properties of the semiconductors, semiconductor heterostructures, graded alloys, quantum liquids, Helium-3 clusters, quantum wells, wires and dots etc. In the present work we obtain several classes of solutions of the one-dimensional Schr\"{o}dinger equation with position-dependent particle mass. As a first step the single particle Schr\"{o}dinger equation with position-dependent mass is transformed into an equivalent Riccati type equation. By considering some integrability cases of the Riccati equation, seven classes of exact analytical solutions of the Schr\"{o}dinger equation are obtained, with the particle mass function and the external potential satisfying some consistency conditions.http://purl.org/coar/access_right/c_14cbSchrodinger equationPosition-dependent massRiccati equationIntegrability conditionsExact solutionsArticulo