Kerimov, G. A.2024-06-122024-06-1220091751-81131751-8121https://doi.org/10.1088/1751-8113/42/44/445210https://hdl.handle.net/20.500.14551/24743We suggest a generalized procedure to obtain exactly solvable position-dependent mass Hamiltonians in one dimension. The second-order Casimir invariant of the regular representation of a non-compact semi-simple Lie group G, the spectral properties of which are well known, is used to introduce exactly solvable Hamiltonians. A brief description of the procedure is presented and its application to quantum systems associated with SL(2, R) is detailed.en10.1088/1751-8113/42/44/445210info:eu-repo/semantics/closedAccessAlgebraic ApproachSchrodinger-EquationElectronsArticle4244Q2WOS:0002709058000172-s2.0-70549112136Q2